Question

2 notepads and 3 boxes of pencils cost $18. And 3 notepads and 2 boxes of pencils cost $17. What is the total cost of 5 notepads and 7 boxes of pencils?

Answer 1

Sub notepads as x and pencils as y

This means that:
Statement 1: 2x + 3y = 18
Statement 2: 3x + 2y = 17

If we multiply statement 1 by 2 and statement 2 by 3 (all variables are multiplied so this will not change anything) then we get:

4x + 6y = 36
9x + 6y = 51

If we subtract the below statement with the above statement we get!

5x = 15

Therefore, x = 3.
Using this we can solve Statement 1 or 2

Statement 1 (x subbed in as 3)
2 x 3 + 3y = 18
6 + 3y = 18
3y = 12
Therefore, y = 4

If we sub this into Statement 2, we can check all our answers (x = 3, y = 4)

3 x 3 + 4 x 2 = 17
9 + 8 = 17
17 = 17 ✅

Therefore, the answers are:
x = 3
y = 4