Question

2. Write an equation to represent each of the following situations.a. A movie theater decreased the size of its popcorn bags by 20%. If the old bags held 15 cups of popcorn, how much do the new bags hold?b. After a 25% discount, the price of a T-shirt was $12. What is the price before the discount?c. Compared to last year, the population of Boom Town has increased by 25%. The population is now 6,600. What was the population last year?

Answer 1

a. The popcorn bags decreased by 20%

The discount is

$15\times\frac{20}{100}=3$

Thus the new bag hold 15-3=12 cups of popcorn.

The answer is 12.

b. Let the original price be x.

Price after discount is 12.

Thus,

$\begin{gathered} x-\frac{25}{100}x=12 \\ \Rightarrow\frac{3}{4}x=12 \\ \Rightarrow x=16 \end{gathered}$

Thus the original price is 16.

c.

Let the original population be x.

It is increased by 25%

Thus,

$\begin{gathered} x+\frac{25}{100}x=6600 \\ \Rightarrow\frac{5}{4}x=6600 \\ \Rightarrow x=5280 \\ \end{gathered}$

Thus the populationlast year was 5280.