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)
Responses

(3,2.6)
left parenthesis 3 comma 2.6 right parenthesis

(5,1)
left parenthesis 5 comma 1 right parenthesis

(0,5)
left parenthesis 0 comma 5 right parenthesis

(−5,9)

Answer 1

To determine a viable solution for the number of robotics kits (y) and chemistry sets (x) that Cindy can purchase with her $50.00 winnings, we can set up the equation based on the costs:

The cost for each robotics kit is $10.00, and the cost for each chemistry set is $8.00. Therefore, the equation for her total spending would be:

\[
10y + 8x = 50
\]

Now, let's evaluate each of the provided options:

1. **(3, 2.6)**:
\[
10(3) + 8(2.6) = 30 + 20.8 = 50.8 \quad (\text{Not viable, exceeds $50.00})
\]

2. **(5, 1)**:
\[
10(5) + 8(1) = 50 + 8 = 58 \quad (\text{Not viable, exceeds $50.00})
\]

3. **(0, 5)**:
\[
10(0) + 8(5) = 0 + 40 = 40 \quad (\text{Viable, under $50.00})
\]
Note: This means she can buy 0 robotics kits and 5 chemistry sets, totaling $40.00, leaving her with $10.00 remaining.

4. **(–5, 9)**:
\[
10(-5) + 8(9) = -50 + 72 = 22 \quad (\text{Not viable, negative robotics kits})
\]

The only viable solution is **(0, 5)**, which means Cindy can purchase 0 robotics kits and 5 chemistry sets.