The sum of two numbers is 188 and the difference is 34. What are the numbers?
How to solve an algebra linear system word problem.
TabletClass Math Academy
Help with Middle and High School Math
Test Prep for High School Math, College Math, Teacher Certification Math and More!
All Courses - TCMathAcademy.com/
✓Help with Middle and High School Math (Public/Private Schools)
✓High School & College Math Test Prep
✓Teacher Certification Math Test Prep
✓Homeschool Math Program and Courses for Pre-Algebra, Algebra 1, Geometry, Algebra 2 and Pre-Calculus.
Popular Math Courses:
Math Foundations
tabletclass-academy.teachable...
Pre-Algebra
tabletclass-academy.teachable...
Algebra
tabletclass-academy.teachable...
Geometry
tabletclass-academy.teachable...
Algebra 2
tabletclass-academy.teachable...
Pre-Calculus
tabletclass-academy.teachable...
Пікірлер: 300
I just found half of 188 to be 94, 94 x 2 = 188, so I added half the difference given (i.e., 34) to one of those 94s and subtracted half the difference from the other. 94 + 17 = 111 and 94 - 17 = 77.
@iceberg54321
7 ай бұрын
Yah that is what I did.
@vincentrobinette1507
3 ай бұрын
I'm glad I saw this reply...I was about ready to post the same thing! To prove you're right, 111+77=188. 111-77=34. If you're like me, it took only as many seconds to figure this out, as the number of minutes this video took to explain it!😎😎
I did in my head - subracted the 34 from 188, divided by 2 for first number, added the 34 for second - 77 & 111.
@angelarhule4239
5 ай бұрын
That’s ow I did it in my head also
@jg-wb3vm
4 ай бұрын
I did it similarly dividing 188 by 2 to get 94, then dividing 34 by 2 and subtracting that from one of my 94s and adding it to the other. Your way is easier.
@clickpositive
3 ай бұрын
Beware in some exams there are marks for method so may well be wanting variable like x. Would depend on the exam.
@debbydechenne172
3 ай бұрын
I did the exact same method. Easy peasy
@chandayadav029
Ай бұрын
That's so helpful more than video
I wish I had a teacher like you when I was in school! I've learned more by watching your videos than I learned in four years of high school. Thank you.
@johnnyD1971
9 ай бұрын
Same
Greetings. The numbers are 111 and 77. We determine the values as follows. We assume that the numbers are X and Y. Thereafter, the sum of these numbers will be ( X +Y) and since we are told that these numbers added is equal to 188, we have X +Y=188. The difference of these numbers equal 34, that is X-Y=34. Now we have two equations with the unknowns X and Y. To determine the values for X and Y, we first eliminate one of the unknowns. We do this by adding the two equations to eliminate Y, that gives 2X = 222, and X = 111. To find the value of Y, we substitute the value for X in either equations. Using equation (2), X -Y = 34 gives 111-Y= 34 and -Y= 34 -111= 77. Lovely.
I divided the 188 and got 94. I divided the 34 and got 17. I then added 17 to 94, getting 111. Then subtracted 111 from 188, getting 77.
@johnnygiraffeeater
9 ай бұрын
I went that way too.
@miraheil5521
9 ай бұрын
The same. Cool.that’s away of a thinking brain
@stevewiley8409
9 ай бұрын
Sheesh...an example of making an easy solution hard..
@anothercitizen4867
9 ай бұрын
Nice mathematical reasoning!
@nelsonx5326
8 ай бұрын
Same. Kind of brute the answer. It worked for this one.
The easiest technique is to halve 188 which gives you 94 then take away half of 34(17) from 94 which leaves 77. 188 - 77 is 111. Therefore 111 and 77 is your answer. Algebra not needed. Just common sense.
@m.h.6470
9 ай бұрын
its far easier to just add 188 + 34 = 222 and then divide by 2 to get 111, which is the first number. For the other number you can either subtract 34 and you get 77 or you subtract the 111 from 188 to get 77.
@marcreider9573
9 ай бұрын
The goal is to find the answer using the tool of algebra, your limitless powers put aside.
@m.h.6470
9 ай бұрын
@@marcreider9573mine is using algebra, just a shortened form of it. x + y = 188 x - y = 34 add both equations and you get 2x = 222 |:2 x = 111 then use that in one of the first equations to get the value of y = 77.
I solved using X + (X + 34) = 188. 2X = 188-34. 2X = 154. X=77. X+ 34 = 111
@retread1083
9 ай бұрын
You know what you're doing, which is good. You're still working with two variables, but you've processed one of them in your head, rather than on paper. That makes it less easy for someone else to follow along. Better, I think, to be verbose and take small steps, rather than leaps. Showing where the (X+34) came from would add clarity. You could start with the second equation and transpose so that y is isolated on the left side. Then show the substitution into the first equation. Also, this part has combining terms, subtracting from both sides, and the result of that subtraction, all occurring in one step: X + (X + 34) = 188. 2X = 188-34. In my opinion, they should be done in separate steps so others can more clearly see what you're doing. -------------------------------------------- [Difference] Y - X = 34 Y - X + X = 34 + X Y = 34 + X Y = X + 34 ------------ (We'll use this now and at the end.) [Sum] X + Y = 188 (substitute) X + (X + 34) = 188. 2X + 34 = 188 2X + 34 - 34 = 188 - 34 2X = 154 X = 77
@nikkitytom
9 ай бұрын
Excellent explanation. I had a page of scribbled equations as I floundered around. Your solution revived my flagging brain in seconds! 👍
@dougnettleton5326
9 ай бұрын
@retread1083 How about? X + Y = 188 X - Y = 34 Add the two equations to get 2 × X = 222 X = 222 / 2 = 111 Y = X - 34 = 111 - 34 = 77
@retread1083
9 ай бұрын
@@dougnettleton5326 That certainly gets to the correct values but if you don't mind, I'll offer some suggestions to improve your presentation. I think it adds clarity if you start a new line for each change, so I'd avoid stringing equalities across the same line. You could add a line when you solve for X to literally show the addition before actually performing the addition. X + Y = 188 X - Y = 34 Add the two equations to get X + Y + X - Y = 188 + 34
@dougnettleton5326
9 ай бұрын
@retread1083 Very funny😂 My original solution was: X + Y = 188 X - Y = 34 Add to eliminate Y 2X = 222 X = 111 Y = 111 - 34 = 77 The deleted stuff was added for clarity. I had a line at the end "No need to write a book" but deleted it. I don't think anyone needing the painful level of detail you provided would be able to work a device where they would encounter the video with the problem.
That was a fun one to figure out. X=111, Y=77. First I tried to reword it so there was only one variable. If X-Y=34, then X=Y+34. From that, you can use (Y+34) to substitute for X. X+Y=188 becomes (Y+34) + Y = 188. Or 2Y+34=188... 2Y=154 ... Y=154/2 ... Y=77. If X=Y+34, then X=111. I did it differently than John, but it works.
Devide the total (188) in half (188/2=94), subtract half of the difference (34) from 94 (94-17=77) and add half of the difference to 94 (94+17=111). The two numbers are 77 and 111.
@TheHawk--oe8iq
8 ай бұрын
I took a different route. I subtracted 34 from 188, leaving 154. Then I divided 154 by 2, giving me 77. Then I added the 34 to 77 to give me the other number, 111. The algebraic equation I used was X + 34 + X = 188, or 2X + 34 = 188, or 2X = 154, or X = 77, and X + 34 = 111.
@annepearson4357
8 ай бұрын
Hey, whatever works for you. If everyone thought and processed things the same way, it'd be a boring world.@@TheHawk--oe8iq
This is much easier than it sounds We have two numbers to find .. but .. we can call them N and N + 34 and we know that N + N + 34 = 188 N + N = 188 - 34 2N = 154 N = 77 and the other number is 77 + 34 = 111
While adding the equations works just as well, I was taught substitution. Solve the first equation for one variable and replace that variable in the second equation.
I figured out the equations but I used a and b and that's as far as I got, the way you figured it out was excellent
The two numbers are 77 and 111. I came up with this answer by subtracting 34 from 188 which gave me 150 for I divided the 154 by 2 to get to equal amounts which were 77 and then I added the 34 back to the 77 to get the 111 that's how I solved it
@light279
9 ай бұрын
Yes, a simple and very logical way to do it in one's head ...it takes about twelve seconds or less.
@asregdor3386
9 ай бұрын
That is what I did right off the get go . Takes seconds to figure it out .
@pilot5298
9 ай бұрын
I did it this way also. Solved mentally in just a few seconds and didn't need a calculator OR algebra.
@eddyrourke5514
9 ай бұрын
I did it similar, I halved 188 and 34 and got 94 and 17, then I added and subtracted 17 from 94.
@andrewmurphy9292
9 ай бұрын
@@eddyrourke5514That's exactly the method I used in my head in well less than a minute.
Solution: x + y = 188 x - y = 34 Add the two equations together to get: x + y + x - y = 188 + 34 2x = 222 |:2 x = 111 x + y = 188 111 + y = 188 |-111 y = 77 The two numbers are 111 and 77.
@theoverlords7960
9 ай бұрын
Systems Of Equations
the sum of means a factor two. or as I do half the 188 and set a plus/ min. Like half both numbers 188/2 + or - 34/2 leads to 94 + 17 and 94 -17
111 and 77 and yes I used algebra. Specifically, started by describing the two true equations resulting from the description, then substituting and resolving for X and Y. Specifically, X+Y=188 and X=Y+34. Then the first equation can be represented as Y+34+Y=188. Then solve for Y. Once you have solved for Y you can immediately solve for X.
i just divided 188 by two in my head, and added half of 34 to it to get the first number. So, (188/2) + (34/2) = 111. Then either subtract 111 - 34 to get 77, or just go (188/2) - (34/2) = 77. Haven't watched the video to see how he did it, but watched far enough to check my answer.
77 and 111. Simply just make two equations. a + b = 188 b - a = 34 Use substitution to find b on one equation and plug it into the other. b = 188 - a (188 - a) - a = 34 188 - 2a = 34 a = 77 Now plug 77 into the other equation. 77 + b = 188 b = 111 Check your work. 77 + 111 = 188 111 - 77 = 34
I just subtracted 34 from 188, divided 154 by 2, got 77 and added the 34 back to one of the numbers.
Haven’t done equations like these since 1970’s. Forgot how much fun they were.
Total / 2 +/- delta / 2. You can use X+Y = 188 and x -y = 34. Do the substitution and solve. But that’s the hard way. Maths uses a lot of shortcuts. Remember the old sum of 1 to 100 numbers…. You can do it the hard way. Or the easy way. Short cuts will save you lots of time when testing, when you have time limits
New to your channel. I would like to begin with some basic skills first. Example- pre- algebra. What are some videos you could suggest to build on to the more advanced lessons.
Got the right answer, but didn’t know the “Algebra” that was shown in the solution. I like the here’s the solution, now how to solve it format. 😊
Enjoyed this one. I did same as charlesstraight below. Your algebra solution made more logical sense though. Tip: if you want to grow your channel more you should interact with the comments, even if you just give the comments a like
I got the right answer. I subtracted 34 from 188 then I took 1/2 of that answer to get 77, added 34 to get 111. Your way was so much easier though .
Dang! You had me puffing out my chest at around the 3:24 mark ... and then hit me with "... but all jokes aside..."
You could emulate the matrix solution, by subtracting 1/1 * equation 1 from equation 2, and show that X is eliminated from all other equations, solve for Y then back-substitute.
I divided 188 by 2 = 94 The divided 34 by 2=17 Then added 94+17=111 And finally subtracted 94-17 =77 Actually, since I did it in my head, I think I mentally subtracted 111 from 188 to get 77 ( it was an easier subtraction)
Excellent lesson. I'm many decades removed from algebra classes and have totally forgotten how to work with linear systems.
@johnemery285
8 ай бұрын
I only took math to Grade 12. I have forgotten most of it. This is a good review but is a bit Greek to me.
Setting up a system of equations of x+y=188 and under that x-y=34 adding the equations together we are left with 2x=222 dividing by 2 gets x=111 plugging 111 into the top equation 111+y=188 subtracting 111 from both sides gets y=77 putting both into second equation 111-77=34 correct thus x=111 y =77
Deduct 34 from 188 = 154 /2 = 77 + 34 =111 + 77= 188 less than 3 seconds to resolve, no algebra required for a problem as basic as this. But thank you for your videos.
Been 57 years since I took an algebra class so I forgot you could add equations. so I did it a different way....draw a line and put zero on the left end and 188 at the other end. Just from logic I can give you 2 numbers that add to 188. Its the one in the middle 188 divided by 2 is 94 , so 94 plus 94=188. to get the right answers split the difference.....34 divided by 2 is 17 so go to 94 and go 17 paces up the road and 17 paces down the road and you have your answers! Yay me.
I added the sum and difference. Then I divided by 2 (just as shown) to get the first number. Afterwards, I subtracted the difference from the sum and divided this by two, and got the second number. Of course, the shown solution is a mathematically correct one and everybody should master it. But mine is faster (with such easy problems).
I did the same as @decosse is this an other system or is it incorrect deduction?
I started by saying x+x+34=188 then taking 34 from each side and tidying up gives 2x=154. Halving each side give one of the numbers as 77. As the sum of both numbers is higher than 77 the other number must be a positive number so I just added 34 to it to get the other number of 111 ------ 2 seconds in my head. well, maybe 3 or 4
(difference + sum) / 2 = the higher of the two numbers 34 + 188 = 222 (difference + sum) 222 / 2 = 111 (gives the higher of the two numbers) 111 - 34 = 77 (subtract the difference to get the lower of the two numbers) 111 + 77 = 188 (test by adding both numbers)
188 Sum of 2 Numbers A 34 Dif of 2 Numbers B 94 Half of 188 A/2 77 Second Number A-(B/2) 111 First Number A+(B/2) 34 111-77 A-B 188 111+77 A+B
Divide 188 and 34 by 2 to get 94 and 17 Subtract 17 from 94 to get 77,add 17 to get 111 I use this method for spread and over/under
Divide both values by 2. 188/2 = 94, 34/2=17. Then subtract 17 from 94 for 77 and add 17 to 94 for 111. This was my mental process.
I subtracted 34 from 188 and divided the 154 (188-34) by 2, giveng me 77. By adding 77 and 34, I get the higher number 111 while using the lower number 77.
111 + 77 = 188; 111-77 = 34 X + Y = 188; X - Y = 34 x = 188 - Y x = 34 + Y 188 - Y = 34 + Y 188 = 34 + Y +Y 188 = 34 + 2Y 188 - 34 = 2Y 154 = 2Y 154/2 =Y 77 = Y
It is interesting that everyone ASSUMES the "difference" means X - Y = 34. But it could be that Y - X = 34. All that is stated is that, "the difference between the two numbers is 34." In either case you get the same NUMBERS, but they get assigned to the opposite variable.
Seems the most facile method for finding the numbers is to use the Gaussian method of variable elimination. The two equations would be: x + y =188 and x - y = 34
I long ago forgot this method of eliminating the y variable. I just did: x+(x-34)=188 >> 2x=222 >> x = 111 >> therefore y=x-34=77
I just took a + b = 188, and added a - b = 34 to it. The result is 2a = 222, therefore a = 111. Substitute 111 for a into either equation for the value of b.
The important lesson is being able to translate the problem into equations.
I divided 188 by 2, added 17 to the sum of 94 and came up with 111, the larger number. Subtracted 17 from the sum of 94 and came up with 77, the smaller number. The total of which is 188.
I used a more literal method for this (did some algebra my style and ended up with x = 94 +-17, x = 111, x = 77
X + Y = 188, & X - Y = 34. Add both equations together. Becomes 2X = 222. (X + X = 2X. Positive Y plus Negative Y cancel out to zero. 188 + 34 = 222; so 2X = 222, divide by 2 becomes X = 111.) So 111 + Y = 188. (Subtract 111 from each side & Y = 188 - 111, or Y = 77.) Answer: 111 and 77. To check if right... 111 + 77 = 188 and 111 - 77 = 34. Is solved and verified to be correct. I used old school algebra. Others below methods of solving is kind of weird to me. But hey if it works for them...
@sonyacotton4881
8 ай бұрын
This is the method I used.
@annepearson4357
8 ай бұрын
Yup. Solve two equations. Old way, but works very well. 😀@@sonyacotton4881
Understood😊👍💥!
Let us write down a equations, what is given: x+y=188 x-y=34 If we add both equations, we get one equation with only one vatiable: (x+y)+(x-y)=188+34 x+y+x-y=222 2*x=222 x=111 We can insert this result inone of the original equations: 111+y=188 => y=188-111=77 or 111-y=34 => y=111--34=77 So the solutionis x=111 and y=77.
Thank goodness. I saw the previous answers and worried I was wrong. I got 111 and 77.
@martinfiedler4317
9 ай бұрын
Same here. 😅
@Real_LiamOBryan
9 ай бұрын
I've gotten into the habit of trying to solve the problem from the thumbnail, then opening the video and using the scrubber to skip to the solution. If I'm right, I don't watch the video unless I I think it might show me a better way of solving the problem; if I'm wrong, however, then I watch pretty much the whole video.
a+b=188 a-b=34 2a=222 A=111 B=77 system of equations add the two equations to isolate a and solve then substitute a to solve for b.
@marcreider9573
9 ай бұрын
I like this explanation, as well.
So this is where Systems of equations come in handy
Let's say the two numbers are x and y x + y = 188 x = y + 34 y + y + 34 = 188 --> 2y = 188 - 34 = 154 --> y = 77 x = y + 34 --> x = 111
Add the two equations and two unknowns Add x +y + x-y = 188 +34. 2x = 222.
The way I used was x+y=188&2x=188-34=154so 2x=154, gives x=77&other value must be 77+34=111
Reading comments everyone is talking about how they got there without algebra. Well I did both but I used the substitution method instead of elimination method. Same answer of course.
I have not looked at the answer as I don't want to waste 18 minutes of my life over a sum that took 2 seconds to work out in my head. Not only was it simple to work out in my head but the equations are so simple to explain that it is incomprehensible to understand what could take 18 minutes to explain - all the best.
The whole purpose of the exercise is to perceive a system of equations and set up the problem accordingly. Since I've been doing these on Khan Academy, it was natural to see the system.
77 and 111, did that in my head in 5 sec: 188 / 2 = 94, 34 / 2 = 17, 94 - 17 = 77 and 94 + 17 = 111
Answer: 1.) A + B=188 or A=188 - B 2.) A -B=34 or A=34 + B 3.) Therefore, 188 -B = 34 + B or 154=2B or 77=B 4.) A + 77 = 188 or 111 + 77 = 188 5.) A = 111 B = 77 6.) Check: 111 + 77 = 188, 111 -77 = 34
Math is so beautiful
The sum of the two numbers is 188. Therefore, draw a number line. Half of the 188 is 94. The differenceof these numbers is 34. Half of 34 is 17. Therefore, to the left of 94 is 94 -17 is 77. And, the right of 94 plus 17 is 111. Thus, 77, 111.
@samo81
9 ай бұрын
That’s basically how I solved it, no pencil needed lol. Yes still used a calculator.
@donitaforrest9064
9 ай бұрын
That's how i solved, but in my head in a few seconds.
@user-qv2dd8ex8k
9 ай бұрын
Yes that is how I solve it until he reminded me to use algebra then I used the substitution method. Not elimination like he did.😁
@maxdriggers
9 ай бұрын
Exactly how I did it. But I did use a calculator.
@tortelvis1
9 ай бұрын
Hi. Can you explain why you cut each number in half? I used substitution method but I would love to understand what you did. Thanks!
I) a + b = 188 II) a - b = 34 I + II) 2a = 222 a = 111 I) b = 188 - a b = 77
a+b = 188. a-b = 34. Add the two equations: 2a = 222. a = 111. b +111 = 188 so b = 77. You don't need 18 minutes to describe this.
X = 1st # Y = 2nd # X + Y = 188 X - Y = 34 2X = 222 X = 111 Y = 188 - 111 = 77 111 + 77 = 188 111 - 77 = 34
111 and 77 ,simultaneous eq
Very basic math calculation using division, subtraction and addition.
Why not just x + (×+34) =188? When you solve for x you get the other number with x+34.
@retread1083
9 ай бұрын
That's the substitution method he briefly mentioned at 12:35 But you've skipped steps to get there.
Add the two numbers and divide by 2. That's 111. Now you need 77 to get to 188. This is a shortcut, but it's not, it's just adding the equations together. Same if you subtracted the equations. It's 188-34 divided by 2 = 77.
I solved this by dividing 188 by 2 which is 94. Then I divided 34 by 2 to get 17. Then I added and subtracted 17 from 94 to get the 2 numbers which are 77 and 111.
Stuff like this I do in my head. Take 188 and cut it in half (94). Then take your 34 and cut it in half (17). Add 17 to 94 and then subtract 17 from 94. There are your two answers (111, 77).
Sum of 2 numbers = 188 and the difference is 34. What are the 2 numbers? x + x + 34 = 188 2x + 34//2 = 188/2 x + 17 = 94 x + 17 - 17 = 94 - 17 x = 77 .. 1st # 2nd # or y = x + 34 y = x + 34 y = 77 + 34 y = 111 *didn’t want to use fractions😊
x + y = 188 x - y = 34 ------------------ 2x + 0 = 222 2x / 2 = 222 / 2 ------------------------- x = 111 111 + y = 188 y = 188 - 111 ------------------------- y = 77 x - y = 34 111 - 77 = 34 34 = 34 ================= x = 111, y = 77
I got it right by in my head in a few seconds - (total - the difference) (difference / 2) (that answer + diff) (188-34=154) ( 154 / 2= 77) (77+34= 111) I would always lose points by not showing my work in class. LOL
I used the simultaneous equation to solve.
In the beginning of the video, the answer is stated as (77,111). Shouldn't the answer be (111,77)? BTW, I really enjoy your videos. You are an excellent teacher!!
Just need to divide by 2 and ad/subtract half of 34.
system of eq 111 and 77
Got it.
I divided 188 by 2 = 94 and divided 34 by 2 =17. 94 + 17 = 111 and 94 - 17 = 77
@pneeb419
9 ай бұрын
Exactly how I solved it.....
Ah heck, no idea. Ill just throw some numbers out there: How about 111 and 77. Just pulled those out of my (hfmmm) I have no idea if that's even right, but I'm gonna go with that.
You sure made that a lot harder than it needs to be. 188/2=94 34/2=17 94-17=77 94+17=111 77+111=188 No paper, no calculator, just 10 seconds of time…if that.
subtract 34 from 188 and divide by 2. add 34 to 1 of the numbers. result, 111 and 77.
Did this in my head and much quicker than the equation. Half is 94 take 17 off and whoop whoop. Can work out the numbers from that 77/111
I did 188 divided by 2=94, then 34 divided by 2=17. 94-17=77. Then 188-77=111. 77 and 111 are the unknown numbers.
They were called simultaneous linear equations when I was at school, and this was a rambling, long-winded way to reach a simple solution.
188-34=154 x=154/2=77 y=77+34=111
Let the numbers be X and Y. The sum is 188-34 = 154. : X+Y = 188- 34= 154 X+ Y= 188-34 = 154. Therefore X + Y =154/2 = 77 The Answer is 77.
Simples....!
I divided 188 in half. 34 in half. I substrates 17 from 94 and added 17 to 94.
I solved this differently. 188 divided by 2 = 94, 34 divided by 2 = 17, 94+17=111, 94-17=77.
THE 2 numbers are 111 and77 but I didn't probably do it the way you are going to do it
got it. 2 formulas & solve for one variable. then sub it.
I just halved the sum (94) then halved the difference (17) added 17 to 94 and subtracted 17 from 94.
X+ Y = 188 X - Y = 34 2X = 222 X = 111 Y = 188 - 111 Y = 77
{94a-60b}= 34
The answers are 116 and 72. X+Y=188 and X-Y=34; Y+Y+34=188
Doesn't seem to be the easy way. Addition is generally easier than subtraction. x = lower number, not higher; x + 34 = y x + x + 34 = 188 2x = 154 x = 77 y = 111 ( from 188 - 77)