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) Responses (3,2.6) left parenthesis 3 comma 2.6 right parenthesis (0,5) left parenthesis 0 comma 5 right parenthesis (−5,9) left parenthesis negative 5 comma 9 right parenthesis (5,1)
To find the viable solution to the number of robotics kits (y) and chemistry sets (x) that Cindy can purchase, we need to solve the equation.
The cost of robotics kits is $10.00 per kit, and the cost of chemistry sets is $8.00 each.
Let's assume Cindy purchases y robotics kits and x chemistry sets. The total cost of the robotics kits is 10y, and the total cost of the chemistry sets is 8x.
Since Cindy spent her entire winnings of $50.00, the equation becomes:
10y + 8x = 50
To find the viable solution, we need to determine the values of y and x that satisfy this equation.
Now, let's look at the given options and substitute the values for y and x:
1) (3,2.6)
If y = 3 and x = 2.6,
The total cost of the robotics kits would be 10 * 3 = $30.00
The total cost of the chemistry sets would be 8 * 2.6 ≈ $20.80
The total cost is 30 + 20.80 ≈ $50.80
Since this exceeds Cindy's winnings, this solution is not viable.
2) (0,5)
If y = 0 and x = 5,
The total cost of the robotics kits would be 10 * 0 = $0.00
The total cost of the chemistry sets would be 8 * 5 = $40.00
The total cost is 0 + 40 = $40.00
Since this is less than Cindy's winnings, this solution is not viable.
3) (-5,9)
If y = -5 and x = 9,
The total cost of the robotics kits would be 10 * (-5) = $-50.00
The total cost of the chemistry sets would be 8 * 9 = $72.00
The total cost is -50 + 72 = $22.00
Since this is more than Cindy's winnings, this solution is not viable.
4) (5,1)
If y = 5 and x = 1,
The total cost of the robotics kits would be 10 * 5 = $50.00
The total cost of the chemistry sets would be 8 * 1 = $8.00
The total cost is 50 + 8 = $58.00
Since this exceeds Cindy's winnings, this solution is not viable.
Therefore, none of the given options is a viable solution.