lpetroski wrote:
For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long?
A. 2.00 + [ \(\frac{0.75r}{2}\) ]
B. 2.00 + 0.75[ \(\frac{r}{2}\) ]
C. 2.00 + 0.75[ r ]
D. 2.00 + [1.5r ]
E. 2.00 + 0.75 [ 2r]
Let r = 1.1 = 1 + 0.1. Since the first 1 mile consists of two 1/2 miles and the last 0.1 mile consists of a fraction of 1/2 mile, we need to pay 3 times $0.75 plus the $2.00 fixed fee. That is, we need to pay 2 + (0.75)(3) = 2 + 2.25 = $4.25.
Now let’s see which answer choice also gives us $4.25 when we substitute 1.1 for r.
A. 2.00 + [0.75r/2] = 2 + [0.75(1.1)/2] = 2 + 1 = $3.00 (notice that 0.75(1.1)/2 is some value between 0 and 1, thus [0.75(1.1)/2] = 1)
B. 2.00 + 0.75[r/2] = 2 + 0.75[1.1/2] = 2 + 0.75 = $2.75 (again notice 1.1/2 is some value between 0 and 1)
C. 2.00 + 0.75[r] = 2 + 0.75[1.1] = 2 + 0.75(2) = $3.50
D. 2.00 + [1.5r] = 2 + [1.5(1.1)] = 2 + 2 = $4.00 (notice 1.5(1.1) is some value between 1 and 2)
We see that none of the first 4 answer choices are correct; therefore, by default, the correct answer must be E. However, let’s verify it anyway.
E. 2.00 + 0.75[2r] = 2 + 0.75[2(1.1)] = 2 + 0.75[2.2] = 2 + 0.75(3) = $4.25
Answer: E
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