SOLUTION: 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 45 feet and walls req

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Question 312410: 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 45 feet and walls requires of paint, find the amount of paint needed to cover the walls of a room with a perimeter of 35 feet and 6-foot walls.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for joint variation is:

z = k*x*y

k is the constant of variation.

Your question is missing some information, so I'll fill in generically and you can apply to your specific problem.

Assume the perimeter is 45 feet and the walls are 3 feet and the amount of paint require is 4 gallons.,

Your formula would then be

4 = 45 * 3 * k

You would solve for k to get:

k = 4 / (45*3) which would make k .02962963

k is your constant of variation and would remain the same.

Now you are given that the perimeter is 35 feet and the walls are 6 feet.

You would solve the following formula:

z = 35 * 6 * k which would become:

z = 35 * 6 * .02962963 which would become:

z = 6.22222222 gallons of paint.

You solved this problem using the joint variation formula.

another way to solve this problem would have been the more conventional way of determining the number of square feet of area that needed to be painted and then determining the amount of paint per square foot.

You were given that 45 feet of perimeter and 3 feet high walls required 4 gallons of paint.

the total square feet to be painted would have been equal to 3 * 45 = 135 square feet.

Since this required 4 gallons, then the amount of paint required per square foot was 4/135 = .02962963 gallons of paint per square foot.

Notice that this is the same as your constant of variation which we called k.

Your new square feet of area that needed to be painted was 35 * 6 = 210 square feet.

210 * .02962963 yielded 6.22222222 gallons of paint.

Since you got the same answer either way you looked at it, the answer looks good.

the joint variation formula, in this case, was the same as determining the square feet of surface that needed to be painted and then applying the amount of paint per square foot to get the answer.