Determine the constant of variation for the stated condition.
-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 70 feet and 10 -foot walls requires 7 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.
A) $4.4$ quarts
B) 440 quarts
C) 44 quarts
D) $8.8$ quarts

Question

Quizplus · Accepted Answer

The constant of variation (k) can be found using the formula for joint variation, $y = kxz$, where y is the amount of paint, x is the perimeter, and z is the height of the walls. Given y = 7 quarts, x = 70 feet, and z = 10 feet, we solve for k: $7 = k(70)(10)$, resulting in $k = \frac{7}{700} = \frac{1}{100}$. To find the amount of paint needed for a perimeter of 55 feet and 8-foot walls, we use $y = \frac{1}{100}(55)(8) = 4.4$ quarts.

Determine the Constant of Variation for the Stated Condition 4.44.44.4 Quarts B) 440 Quarts C) 44 Quarts D)

Determine the Constant of Variation for the Stated Condition $4.4$ Quarts
B) 440 Quarts
C) 44 Quarts
D)