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.
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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
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