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)

Answer 1

To determine a viable solution for the number of robotics kits and chemistry sets Cindy can purchase, we need to set up and solve the equation based on her total winnings:

Let:
- \( y \) = number of robotics kits
- \( x \) = number of chemistry sets

The cost of a robotics kit is $10.00 and the cost of a chemistry set is $8.00, with a total budget of $50.00. The equation can be represented as:

\[
10y + 8x = 50
\]

We'll analyze the given response options to see if they satisfy this equation.

1. **(3, 2.6)**:
\[
10(3) + 8(2.6) = 30 + 20.8 = 50.8 \quad (\text{not a solution})
\]

2. **(5, 1)**:
\[
10(5) + 8(1) = 50 + 8 = 58 \quad (\text{not a solution})
\]

3. **(−5, 9)**:
\[
10(-5) + 8(9) = -50 + 72 = 22 \quad (\text{not a solution})
\]

4. **(0, 5)**:
\[
10(0) + 8(5) = 0 + 40 = 40 \quad (\text{not a solution})
\]

None of the given options satisfy the equation \( 10y + 8x = 50 \).

However, let's further clarify criteria for solutions. Since \( y \) and \( x \) must be non-negative integers (as you can't purchase a negative quantity or fractional kits), none of the provided answers fit this criterion.

To check for valid integer solutions:
- If Cindy bought only robotics kits (\( x = 0 \)):
\[
10y = 50 \quad \Rightarrow \quad y = 5
\]
- If Cindy bought only chemistry sets (\( y = 0 \)):
\[
8x = 50 \quad \Rightarrow \quad x = 6.25 \quad (\text{not an integer})
\]

Thus, suitable combinations could be (for integer values):
- (5, 0): 5 robotics kits and 0 chemistry sets.
- (4, 1): 4 robotics kits and 1 chemistry set.
- (3, 2): 3 robotics kits and 2 chemistry sets.
- (2, 3): 2 robotics kits and 3 chemistry sets.
- (1, 4): 1 robotics kit and 4 chemistry sets.
- (0, 5): 0 robotic kits and 5 chemistry sets.

The integers that satisfy the budget will need to be analyzed from these possible combinations. But again, from the provided options, none are viable solutions.