Question

A city currently has 60 family-owned restaurants. In the future, it is estimated that the number of those restaurants will decline at a rat of 18% per year. Based on that estimate, what is the fewest number of years it will take for there to be less than 20 family-owned restaurants in the city? A.1 B. 3 C. 4 D. 6

Answer 1

The correct answer is D. 6

Explanation:

To know precisely how the number of restaurants in the city decreases over time, it is necessary to determine the 18% of the total of restaurants each year and to subtract this number. The process year per year is shown below:

First-year- 60 restaurants- Find the percentage by writing the known value and using cross multiplication

$60 = 100$ %

$x = 18$%

$x 100 = 60 x 18$

$x = \frac{1080}{100}$

$x = 10.8$   Number of restaurants that were closed

$60-10.8 = 49.2$ New total

Second-year - 49.2 restaurants- Repeat te process

$x = \frac{49.2x 18}{100}$ Shortened version of the equation. Total of restaurants, multiplied by percentage and divided into 100 (total percentage)

$x = 8.8$

$49.2 - 8.8 = 40.4$ New total

Third-year- 40.4 restaurants

$x = \frac{40.4 x 18}{100}$

$x = 7.2$

$40.4-7.2 = 33.2$  New total

Fourth-year- 33.2 restaurants

$x = \frac{33.2x 18}{100}$

$x = 6.3$

$33.2- 6.3= 26.9$ New total

Fifth-year- 26.9 restaurants

$x = \frac{26.9 x 18}{100}$

$x = 4.8$

$26.9-4.8 = 22.1$ New total

Sixth-year- 22.1 restaurants

$x = \frac{22.1x 18}{100}$

$x= 3.96$

$22.1-3.9 = 18.1$

According to this at this rate, it will take at least 6 years for the number of restaurants to be below 20.