Question

The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room and the height of the wall. If a room with a perimeter of 35 feet and 10 dash foot walls requires 3.5 quarts of​ paint, find the amount of paint needed to cover the walls of a room with a perimeter of 55 feet and 8​-foot walls.

Answer 1

4.4 quarts of paint needed to cover the walls of a room with a perimeter of 55 feet and 8​-foot walls

Solution:

Given that,

The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room and the height of the wall

The formula for joint variation is:

$z = k \times x \times y$

Where,

z is the amount of paint needed

x is the perimter of room

y is the height of room

Room with a perimeter of 35 feet and 10 foot high walls requires 3.5 quarts of​ paint

Therefore,

$3.5 = k \times 35 \times 10\\\\ k = \frac{3.5}{350}\\\\k = 0.01$

find the amount of paint needed to cover the walls of a room with a perimeter of 55 feet and 8​-foot walls

Substitute k = 0.01, x = 55 and y = 8 in joint variation formula

$z = 0.01 \times 55 \times 8\\\\z = 4.4$

Thus, 4.4 quarts of paint needed to cover the walls of a room with a perimeter of 55 feet and 8​-foot walls