2012 CEMC Gauss (Grade 8) Problems/Problem 16

Problem

A parking lot has $25\%$ more cars than trucks. The ratio of cars to trucks is

$\text{ (A) }\ 4 : 3 \qquad\text{ (B) }\ 4 : 1 \qquad\text{ (C) }\ 9 : 5\qquad\text{ (D) }\ 5 : 4 \qquad\text{ (E) }\ 3 : 1$

Solution 1

Let $t$ be the number of trucks, and $c$ be the number of cars. Since there are $25\%$ more cars than trucks, we have:

$c = 0.25t + 1.00t = 1.25t$

Thus, the ratio of cars to trucks is:

$c : t = 1.25t : t = \boxed {\textbf {(D) } 5 : 4}$

~anabel.disher

Solution 2

We can pick an easy number to find the ratio with. Let $4$ be the number of trucks, and let $c$ be the number of cars. Since there are $25\%$ more cars than trucks, we have:

$c = 0.25 \times 4 + 1.00 \times 4 = 5$

Thus, the ratio of cars to trucks is

$c : 4 = \boxed {\textbf {(D) } 5 : 4}$

~anabel.disher

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2012 CEMC Gauss (Grade 8) Problems/Problem 16

Problem

Solution 1

Solution 2