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?
• (5,1)
• (-5,9)
• (3, 2.6)
• (0,5)
In order to find the viable solution, we must set up an equation based on the given information.
Let the number of robotics kits be represented by y and the number of chemistry sets be represented by x.
The cost of the robotics kits is $10.00 per kit, so the cost of y robotics kits is 10y.
The cost of the chemistry sets is $8.00 per set, so the cost of x chemistry sets is 8x.
Since Cindy spent her entire winnings of $50.00, the total cost of the robotics kits and chemistry sets must be equal to $50.00.
Therefore, the equation is:
10y + 8x = 50
Now let's check which solution satisfies the equation.
Option (5,1):
10(5) + 8(1) = 50
50 + 8 = 58 ≠ 50
Option (-5,9):
10(-5) + 8(9) = 50
-50 + 72 = 22 ≠ 50
Option (3,2.6):
10(3) + 8(2.6) = 50
30 + 20.8 = 50.8 ≠ 50
Option (0,5):
10(0) + 8(5) = 50
0 + 40 = 40 ≠ 50
None of the options satisfy the equation 10y + 8x = 50.
Therefore, there is no viable solution provided in the given options.