Question

The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched (a) in sq ft and the depth of the mulch (d) in feet. If you need 10 bags to mulch 120ft to a depth of 3in. How many bags do you need to mulch 200ft to a depth of 4in? HELPPP ASAP WILL GIVE BRAINLIST !!!

Answer 1

Answer:

  22 2/9

Step-by-step explanation:

When z "varies jointly" with x and y, it can be described by the formula

   z = kxy

Here, we have bags of mulch (n) varying jointly with area (a) and depth (d), both in feet. The given information can let us find the value of k.

  n = kad

  10 = k·(120)(1/4)

  10/30 = k = 1/3 . . . . . divide by the coefficient of k

Now, we can fill in the other values of interest.

  n = (1/3)·(200)·(1/3) = 200/9

  n = 22 2/9

You need 22 2/9 bags of mulch to cover 200 ft² to a depth of 4 inches.

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Comment on the problem

This problem requires the formula be written with both area and depth expressed in feet, yet it gives depth in inches. The formula can also be written using depth in inches. In that case, k = 1/36.