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

Step-by-step 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 = (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 = (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 = (40.4 x 18)/(100)`

`x = 7.2`

`40.4-7.2 = 33.2` New total

Fourth-year- 33.2 restaurants

`x = (33.2x 18)/(100)`

`x = 6.3`

`33.2- 6.3= 26.9` New total

Fifth-year- 26.9 restaurants

`x = (26.9 x 18)/(100)`

`x = 4.8`

`26.9-4.8 = 22.1` New total

Sixth-year- 22.1 restaurants

`x = (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.