Use the table to answer the question. Adults Children 0 250 80 100 47 161.175 68.8 121 Entrance to the water park costs $15 per adult and $8 per child. Today, there are a mix of adults and children at the park, with income from entrance fees totaling $2,000. Which of the values in the table represents a viable solution? The value for Adults is represented by the x coordinate and the value for Children is represented by the y coordinate. (1 point) Responses (47,161.175) left parenthesis 47 comma 161.175 right parenthesis (80,100) left parenthesis 80 comma 100 right parenthesis (68.8,121) left parenthesis 68.8 comma 121 right parenthesis (0,250)

Answer 1

To find the viable solution from the table, we need to set up an equation based on the income generated from the entrance fees. The costs are $15 per adult and $8 per child, and the total income from entrance fees is $2,000.

We can represent the total income with the following equation:

\[ 15x + 8y = 2000 \]

where \( x \) is the number of adults and \( y \) is the number of children.

Now, we can substitute the pairs of values from the table into this equation to see which one satisfies it.

1. For (47, 161.175): \[ 15(47) + 8(161.175) = 705 + 1289.4 = 1994.4 \] (not valid)

2. For (80, 100): \[ 15(80) + 8(100) = 1200 + 800 = 2000 \] (valid)

3. For (68.8, 121): \[ 15(68.8) + 8(121) = 1032 + 968 = 2000 \] (valid)

4. For (0, 250): \[ 15(0) + 8(250) = 0 + 2000 = 2000 \] (valid)

Thus, the pairs that give a total income of $2,000 are (80, 100), (68.8, 121), and (0, 250).

Since the question asks for a viable solution, we see that multiple pairs are correct, but the first valid choice is (80, 100).

Final Answer: (80, 100)