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:
[tex]z = k \times x \times y[/tex]
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,
[tex]3.5 = k \times 35 \times 10\\\\ k = \frac{3.5}{350}\\\\k = 0.01[/tex]
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
[tex]z = 0.01 \times 55 \times 8\\\\z = 4.4[/tex]
Thus, 4.4 quarts of paint needed to cover the walls of a room with a perimeter of 55 feet and 8-foot walls
