Creating Two-Variable Equations Quick Check

Question

5 of 55 of 5 Items
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

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

(0,5)
left parenthesis 0 comma 5 right parenthesis
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Answer 1

To determine which response is a viable solution to the number of robotics kits (y) and chemistry sets (x) that Cindy can purchase with her winnings, we need to set up the equation based on the given prices. The total cost can be expressed as:

\[ 10y + 8x = 50 \]

Now, let's evaluate each option:

1. (3, 2.6): \[ 10(2.6) + 8(3) = 26 + 24 = 50 \] This solution is viable.

2. (5, 1): \[ 10(1) + 8(5) = 10 + 40 = 50 \] This solution is viable.

3. (−5, 9): \[ 10(9) + 8(-5) = 90 - 40 = 50 \] This solution is not viable because the number of robotics kits cannot be negative.

4. (0, 5): \[ 10(5) + 8(0) = 50 + 0 = 50 \] This solution is viable.

Viable solutions must involve non-negative integers. Therefore, the viable solutions from the choices given are:

• (3, 2.6) - Not viable because 2.6 is not an integer.
• (5, 1) - Viable
• (−5, 9) - Not viable because of the negative.
• (0, 5) - Viable

Thus, the correct options that are viable solutions would be (5, 1) and (0, 5).

However, if you need just one solution, (5, 1) is a perfect choice as it uses the entire amount without any fractions.