Question

Cindy won $50.00 for getting first place in the Science Fair. She spent her winnings on robotics kits and chemistry sets. Each robotics kit (y) costs $10.00, while each chemistry set costs $8.00 (x). Which of the following is a viable solution to the number of robotics kits and chemistry sets Cindy can purchase, assuming she spends her entire winnings?(1 point)

(−5,9)


(5,1)


(3,2.6)


(0,5)

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Answer 1

Let x = number of chemistry sets and y = number of robotics kits. Cost equation: 8x + 10y = 50.

Check each pair:
- (−5,9): 8(−5)+10(9)=50 but x = −5 is not allowed (can't buy negative sets).
- (5,1): 8(5)+10(1)=40+10=50 — valid (both nonnegative integers).
- (3,2.6): 8(3)+10(2.6)=24+26=50 but y = 2.6 is not an integer (can't buy part of a kit).
- (0,5): 8(0)+10(5)=50 — valid.

Viable solutions: (5,1) and (0,5).