Middle School

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A theater has 82 seats.

If the theater sells out all its seats for $18 a seat, which would be the best strategy for estimating the total amount of money received?

A. 15 × 80
B. 15 × 85
C. 20 × 80
D. 20 × 85

Answer :

Final answer:

To estimate the total revenue of a theater with 82 seats selling at $18 each, the best estimation strategy, which balances accuracy with ease of computation, is to approximate both the price and seat count. The most suitable option is 20 x 80, which provides a reasonable estimate without overestimating the total revenue.

Explanation:

The student is presented with a problem from the realm of Mathematics, specifically focused on estimation and multiplication concepts. Given a theater with 82 seats and a ticket price of $18 per seat, the best estimation strategy for calculating total revenue would be to find a product that is closest to the actual result without going over. The strategy of choosing an estimated multiplication that has factors close to the actual numbers, while still being easier to compute, will yield a sufficient estimate for an initial assessment of total income.

Considering the options provided to estimate the total revenue, let's break them down:

  • Option A: 15 x 80
  • Option B: 15 x 85
  • Option C: 20 x 80
  • Option D: 20 x 85

Option A (15 x 80) underestimates both the number of seats and the price per seat. Option B (15 x 85) gets closer to the number of seats but still underestimates the ticket price. Option D (20 x 85) overestimates both the number of seats and ticket price, leading to an overestimation of the total revenue. Hence, the best strategy is Option C (20 x 80), which multiplies a rounded-up ticket price by a rounded-down number of seats, leading to a close estimate that does not significantly overestimate the total.

Applying this approach:

20 x 80 = 1,600

This figure represents the total revenue assuming each seat is approximated to cost $20, and the total number of seats is estimated to be 80, which gives a balanced estimate without being overly precise or time-consuming.

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