Question

The height of a building is proportional to the number of floors. The figure shows the height of a building with 7 floors. Complete parts a and b. h equals 98 ft a. Write the ratio of height of the building to the number of floors.​ Then, find the unit​ rate, and explain what it means in this situation.

Answer 1

Answer:

a. The ratio of the height of the building to the number of floors is $\frac{98}{7}$

b. The unit rate is 14 feet per floor. The unit rate is the constant of proportionality in this situation

Step-by-step explanation:

Proportional relationships are relationships between two variables where their ratios are equivalent

Example; If y is proportion to x, then $\frac{y}{x}$ = constant ratio, this constant ratio is called the constant of proportionality

∵ The height of a building is proportional to the number of floors

- If the height is h and the number of floors is n

∴ $\frac{h}{n}$ = k, where k is the constant of proportionality

∵ The building is 7 floors

∴ n = 7

a.

∵ The height of the building is 98 feet

∴ h = 98

∵ n = 7

∴ $\frac{h}{n}=\frac{98}{7}$

∴ The ratio of the height of the building to the number of floors is $\frac{98}{7}$

b.

To find the unit rate divide the both terms of the ratio by 7

∵  $\frac{h}{n}=\frac{98}{7}$

∴  $\frac{h}{n}=\frac{98/7}{7/7}$

∴  $\frac{h}{n}=\frac{14}{1}$

∴ The unit rate is 14 feet per floor

The unit rate is the constant of proportionality in this situation