Question

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

(−5,9)
left parenthesis negative 5 comma 9 right parenthesis

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

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

(3,2.6)
left parenthesis 3 comma 2.6 right parenthesis
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Answer 1

To determine which of the given pairs \((x, y)\) (where \(x\) is the number of chemistry sets and \(y\) is the number of robotics kits) is a viable solution, we need to set up the equation based on Cindy's budget:

The total cost of the chemistry sets and robotics kits must equal her winnings:

\[
8x + 10y = 50
\]

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

1. **\((-5, 9)\)**:
\[
8(-5) + 10(9) = -40 + 90 = 50 \quad \text{(Valid equation, but cannot buy negative chemistry sets)}
\]
This is not viable.

2. **\((5, 1)\)**:
\[
8(5) + 10(1) = 40 + 10 = 50 \quad \text{(Valid solution)}
\]
This is viable.

3. **\((0, 5)\)**:
\[
8(0) + 10(5) = 0 + 50 = 50 \quad \text{(Valid solution)}
\]
This is also viable.

4. **\((3, 2.6)\)**:
\[
8(3) + 10(2.6) = 24 + 26 = 50 \quad \text{(Valid equation, but cannot buy partial kits)}
\]
This is not viable.

Thus, the viable solutions from the options given are \((5, 1)\) and \((0, 5)\).