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PCAT Quantitative Reasoning – Fence Perimeter

A fence-building company charges either by the amount of materials required or by the number of labor hours, whichever is cheaper. When charging by the amount of materials required, the company currently charges $60 per meter of fencing. When charging by the hour, the company charges $26 per hour of labor plus a base price of $128. If it takes half an hour to erect 1 meter of fencing, what is the minimum length a fence can be for the company to charge by the hour?

  1. 4 m
  2. 8 m
  3. 12 m
  4. 16 m
Click for Explanation

D is correct. To solve this word problem, we need to translate it into an inequality. On one hand, the company charges $60 per meter of fencing ($60x). On the other hand, the company charges $26 per hour plus a base of $128 ($26h + $128). We are interested in circumstances when the latter term is cheaper, or smaller, than the first term:

$60x > $26h + $128

Next, we need to use substitution to make all the variables consistent. We are told that each meter of fencing takes a half-hour to build, or that two meters of fencing can be built in one hour:

x = ½ h

h = 2x

Let’s substitute in 2x for h and solve:

$60x > $26(2x) + $128

$60x > $52x + $128

$8x > $128

x > 16 m

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