A high school theater teacher estimates that the theater students will sell 520

Question

tickets to the school play. The theater students actually sell 600
tickets to the school play.

Which statement is true?

Responses

The theater teacher overestimates the ticket sales by approximately
.

The theater teacher overestimates the ticket sales by approximately 13.3 % % .

The theater teacher overestimates the ticket sales by approximately
.

The theater teacher overestimates the ticket sales by approximately 15.4 % % .

The theater teacher underestimates the ticket sales by approximately
.

The theater teacher underestimates the ticket sales by approximately 13.3 % % .

The theater teacher underestimates the ticket sales by approximately
.

Answer 1

To determine whether the theater teacher overestimated or underestimated the ticket sales and by how much, we can calculate the percentage difference between the estimated and actual ticket sales.

1. Estimated ticket sales: 520
2. Actual ticket sales: 600

Since the actual sales (600) are greater than the estimated sales (520), this means the teacher underestimated the ticket sales.

To find the percentage difference:

\[ \text{Difference} = \text{Actual} - \text{Estimated} = 600 - 520 = 80 \]

Next, we calculate the percentage of the estimated amount:

\[ \text{Percentage Underestimate} = \left( \frac{\text{Difference}}{\text{Estimated}} \right) \times 100 = \left( \frac{80}{520} \right) \times 100 \]

Now we calculate:

\[ \frac{80}{520} \approx 0.153846 \]

\[ 0.153846 \times 100 \approx 15.38 \]

So, the theater teacher underestimates the ticket sales by approximately 15.4%.

The correct statement is:

The theater teacher underestimates the ticket sales by approximately 15.4%.