Question

The volume of paint used, V liters, is directly proportional to the area, A square feet, that the paint can cover. 5 liters of paint can cover a wall with an area of 75 square feet.

Answer 1

Question Completion

a) Find the constant of proportionality.

b) Write an equation relating V and A.

c) How much paint would be needed to cover an area of 180 square feet? Answer:

`(a)k=(1)/(15) \\\\(b)V=(1)/(15)A`

(c)12 Liters

Explanation:

The volume of paint used, V liters, is directly proportional to the area, A square feet, that the paint can cover.

This is written as:

`V \propto A\\V=kA,$ where k is the constant of proportionality`

(a)5 liters of paint can cover a wall with an area of 75 square feet.

V=5 liters, A=75 square feet.

Substitution into V=kA

5=75k

k=5/75

`\text{Constant of proportionality, k}=(1)/(15)`

(b)Substitution of
`k=(1)/(15)` into V=kA

The equation relating V and A is:

`V=(1)/(15)A`

(c)If A=180 Square feet

Volume of paint needed,

`V=(1)/(15) X 180\\=12$ liters`