Thread: Another word problem

The sum of two numbers is 42. One number plus two times the other number is 57. What are the two numbers?

I need the formula as well to help me learn to disect these problems. I have a block or something. Is there an easy way to learn this!!!! Age problems are worse!

try to write mathematical equations from the information provided.
Let us call 1 of the numbers x and the other y. now try to do it and I will correct you.

This is the formula I think. I just don't know how to solve it without
more information


x+2y=42

Originally Posted by Nicv

The sum of two numbers is 42.

x + y = 42

Originally Posted by Nicv

One number plus two times the other number is 57..

x + 2y = 57

can you take it from here?

Nope, sorry.

OK, no problem,

First is important that you understand where these equations come from.

x + y = 42
x + 2y = 57

Once you understand how I wrote these equations from the given information we can solve this system of equations using substitution or subtracting the top equation from the bottom and then using substitution.

..(x + 2y = 57)
-(x + y = 42)
........y = 15

now plug in y=15 into either equation above and solve for x. Give it a try and I will correct you if you make a mistake.

that totally makes sense now. what happens in this case?

x-y=80
3x=4y=-334

i appreciate your help. i am taking an online course and this self teaching isn't
really working for me. no worries i don't hand any of this in!

x-y=80
3x+4y=-334

Lets solve for x in terms of y on the first equation and then plug it in to the second.

x-y=80
x=y+80 eq1

3x+4y=-334 (plug in eq1 for x)
3(y+80)+4y=-334
3y+240+4y=-334
7y=-574
y=-82

now plug in y to the first equation
x-(-82)=80
x=-2

Here is one way.

"The sum of two numbers is 42. One number plus two times the other number is 57. What are the two numbers?"

Let x = one number
So, 42-x is the other number

x +2(42-x) = 57
x +84 -2x = 57
x -2x = 57 -84
-x = -27
x = 27

42-x = 42-27 = 15

Therefore, the two numbers are 15 and 27. ----answer.

----------------
Another way.

Let x = one number
And y = the other number

x +y = 42 ----(i)
x +2y = 57 ----(ii)

From (i), x = 42-y
Substitute that into (ii),
(42-y) +2y = 57
42 -y +2y = 57
-y +2y = 57 -42
y = 15

So,
x = 42-y = 42-15 = 27

Therefore, the two numbers are 15 and 27.

Or,
(ii) minus (i),
y = 15 ----right away.
etc...