Official Guide Explanation:
Problem Solving #68




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Solution and Metadata

Question: 68
Page: 161
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Functions > other
Category 2: Algebra > Linear Equations-One Unk >

Explanation: Any time you see a word problem this long, especially with a formula given, trust that it will not ultimately be that complicated. Your main task is sifting through all the information and finding the straightforward math problem hidden inside.

Given the formula for N, we need values of L, d, and s. The question tells us that L = 2 and s = 40. It also tels us that the length of the portion of the highway is (1/2)mile, though d needs to be in feet. Since it's given that 1 mile equals 5,280 feet, (1/2) mile is 2,640 feet, so d = 2,640. Plug in these three values:

N = ((20Ld)/(600 + s2))

= ((20(2)(2,640))/(600 + 402))

= ((40(2,640))/(600 + 1600))

= ((40(2,640))/2200)

= ((4(264))/22)

= ((2(264))/11) = (528/11)

We don't need to find the exact value of the fraction. If the numerator were 550, the value would be 50. The only answer choice even remotely in the same range is (D), 48.

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