Question

the sum of two numbers is 31. The first is 5 less than the second. Find the numbers.

Answer 1

Can you convert this into an equation?

Answer 2

x=5-y ??

Answer 3

Not quite, it's \(x = y - 5\) (making \(y\) 5 less than \(x\)).

Answer 4

So that's the first part, what about the part where it says that `the sum of two numbers is 31'. Can you make that into an equation?

Answer 5

x+y=31

Answer 6

Right. So now you have two equations:

\[\begin{align}
x + y &= 31\\
y - 5 &= x
\end{align}\]

Answer 7

Can you solve that system of equations?

Answer 8

y-5+y

Answer 9

=31

Answer 10

Right, and then can you solve that equation for y?

Answer 11

that is where i am a little confused. do i minus a y?

Answer 12

4y?

Answer 13

So you have:

y - 5 + y = 31

You can put the ys together:

y + y - 5 = 31

Which is the same as:

2y - 5 = 31

Answer 14

2y=26?

Answer 15

Not quite, remember that if we want to move the 5 over to the right, you have to add 5 to both sides to cancel it on the left:

2y - 5 + 5 = 31 + 5
2y = 36

Answer 16

oh so i have to add 5 to equal it out since it is negative?

Answer 17

Exactly.

Answer 18

thats where i went wrong. y=18?

Answer 19

Exactly.

Answer 20

And then what's x?

Answer 21

x=18-5=13

Answer 22

13

Answer 23

Exactly!

Answer 24

thank you. i am going to attempt my next problem.

Answer 25

Cool.