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:

$(a)k=\frac{1}{15} \\\\(b)V=\frac{1}{15}A$

(c)12 Liters

Step-by-step 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

$\text{Constant of proportionality, k}=\dfrac{1}{15}$

(b)Substitution of $k=\dfrac{1}{15}$ into V=kA

The equation relating V and A is:

$V=\frac{1}{15}A$

(c)If A=180 Square feet

Volume of paint needed,

$V=\frac{1}{15} X 180\\=12 liters$