Question

mr. granger wants to spread fertilizer on his vegetable garden that has dimensions 41.5 feet by 30.8 feet. the fertilizer he chose costs $0.75 per square - foot for coverage. what is the possible range for the cost of the fertilizer that is needed to cover the vegetable garden? the cost would be at least $958.65 but less than select choice $958.65 $960.82 $961.36 $964.80

Explanation:

Step1: Calculate the area of the garden

The area \(A\) of a rectangle is \(A = l\times w\), where \(l = 41.5\) ft and \(w=30.8\) ft. So \(A=41.5\times30.8 = 41.5\times(30 + 0.8)=41.5\times30+41.5\times0.8=1245+33.2 = 1278.2\) square - feet.

Step2: Calculate the cost of the fertilizer

The fertilizer costs \(0.75\) dollars per square - foot. So the total cost \(C\) is \(C = 0.75\times A\). Substitute \(A = 1278.2\) into the formula: \(C=0.75\times1278.2=( \frac{3}{4})\times1278.2 = 1278.2\div4\times3=319.55\times3 = 958.65\) dollars. Since the cost is at least \(958.65\) dollars but less than some value, and we know the lower - bound value of the cost.

Answer:

The cost is at least \(958.65\) dollars but less than \(960.82\) (as \(958.65<960.82\) and among the given options \(960.82\) is the next value greater than \(958.65\)). So the possible range is from \(958.65\) to \(960.82\).