Question

Harry had $32. He spent all the money buying three notebooks for x dollars each and four packs of index cards for y dollars each. If Harry had bought five notebooks and five packs of index cards, he would have run short by $18. The following system of equations models this scenario: 3x + 4y = 32 5x + 5y = 50 Use the system of equations to solve for x and y.

Answer 1

Answer:

x = 8 and y = 2

Step-by-step explanation:

3x + 4y = 32 ...(1) multiplying by 5

5x + 5y = 50. ....(2) multiplying by 3

15x + 20y = 160. .....(3)

15x + 15y = 150. ......(4)

Subtracting (4) from (3)

15x + 20y = 160. .....(3)

15x + 15y = 150. ......(4)

- -. -. (sign changes due to subtraction)

0 + 5y = 10

5y = 10

y = 2

Substituting y = 2 in (2)

5x + 5(2) = 50

5x + 10 = 50

5x = 50 - 10

5x = 40

x = 40/5

x = 8

x = 8 and y = 2

I hope it helps