the sum of two numbers is 15 and the difference is 7

Answer 1

Let the numbers be x and y

X + Y =15

X -Y = 7

Make X subject of formula in equation 1

X = 15-Y

Substitute for X in equation 2

15 -Y -Y = 7

15 - 2Y = 7

15 - 7 = 2Y

8 = 2Y

Divide both sides by 2

Y = 4

Substitute for Y in equation 3

X=15 -Y

X=15-4

X=11

Therefore the numbers are 11 and 4

Answer 2

Hi Kimberly,

One way to solve this problem is to reason about the possible answers:

"The sum of two numbers is 15"

We can list the possible numbers that combine to form a sum of 15.

1+14

2+13

3+12

4+11

5+10

6+9

7+8

It is also possible that one of the numbers is negative.

16+-1

17+-2

18+-3

19+-4

20+-5

21+-6

22+-7

This list is infinite, as we can simply keep counting up.

"And the difference is 7."

In the above lists, are there any pairs of numbers that, if you were to subtract one from other other, their difference is 7? I see one pair in the list of positive numbers where the difference is 7.

In the list of positive numbers paired with negative numbers, the differences start at 17 and grow from there. So there are no possible answers on that list.

I hope that helps! If this answer was helpful, please upvote it.