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

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

Harry's money is $ 32

He said that he spent ALL of his money buying 3 Notebooksx and 4 cards y, so the equation that represent this is  
3x + 4y = 32 .

He said that HE IS SHORT $18 if he wants to buy 5 notebook x and 5 cards y,
So the equation that represent this is
5x + 5y = 32 + (18)
5x + 5y = 50

And (8,2) is the only one that fit in both equation/