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)

(3,2.6)


(0,5)


(5,1)


(−5,9)

Answer 1

Let x = number of chemistry sets ($8 each) and y = number of robotics kits ($10 each). The cost equation is 8x + 10y = 50, with x,y nonnegative integers.

Check each pair (x,y):
- (3, 2.6): 8(3) + 10(2.6) = 24 + 26 = 50, but y = 2.6 is not an integer (can't buy 0.6 of a kit) → not viable.
- (0, 5): 8(0) + 10(5) = 0 + 50 = 50 → viable.
- (5, 1): 8(5) + 10(1) = 40 + 10 = 50 → viable.
- (−5, 9): x = −5 is negative (can't buy negative sets) → not viable.

So the viable solutions are (0, 5) and (5, 1).