Question

Harry had $32. He spent all the money on buying 3 notebooks for $x each and 4 packs of index cards for $y each. If Harry had bought 5 notebooks and 5 packs of index cards, he would have run short of $18.
A student concluded that the price of each notebook is $5 and the price of each pack of index cards is $1. Which statement best justifies whether the student's conclusion is correct or incorrect?

The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2).
The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (8, 2).
The student's conclusion is correct because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (5, 1).
The student's conclusion is correct because the solution to the system of equations 3x − 4y = 32 and 5x − 5y = 50 is (5, 1).

Answer 1

3x + 4y = 32....multiply by 5
5x + 5y = 50...multiply by -3
---------------
15x + 20y = 160 (result of multiplying by 5)
-15x - 15y = -150 (result of multiplying by -3)
--------------add
5y = 10
y = 10/5
y = 2

3x + 4y = 32
3x + 4(2) = 32
3x + 8 = 32
3x = 32 - 8
3x = 24
x = 24/3
x = 8

solution (8,2)

The students conclusion is incorrect......it is answer choice 1