SAT problem of the week, September 01, 2014 Solution

Hint for process of elimination: The problem asked for the price, in cents, of 1000 fluid ounces of diesel fuel. We are told in the problem, and you may also remember from science class, that there are 128 fluid ounces in one gallon. That means there are 1280 fluid ounces in ten gallons. 1000 ounces is a little less than ten gallons, but not much less. It follows that the price in dollars of the 1000 fluid ounces is a little less than $latex D &s=1$. Therefore, the price in cents of 1000 fluid ounces is a little less than $latex 100D &s=1$. The only answer with a coefficient of D that is close to but less than $latex 100 &s=1$ is choice D.

Read on for a full solution.

Answer: D

Solution: We need the price of 1000 ounces of diesel fuel. We can first find the price per ounce. The word “per” means division, so the rate is $latex \dfrac{\text{price }}{\text{quantity}} &s=1$. Let’s use conversion factors to convert the price in dollars per gallon to the price in cents per ounce

$latex \dfrac{D\text{ dollars}}{10\text{ gal}} \times \dfrac{1\text{ gal}}{128\text{ fl oz}} \times \dfrac{100\text{ cents}}{1\text{ dollar}} = \dfrac{100D\text{ cents}}{1280\text{ fl oz}} = \dfrac{5D}{64} \text{cents/fl oz} &s=1$

If we multiply both sides of the rate equation $latex \left( \text{rate} = \dfrac{\text{price}}{\text{quantity}} \right)&s=1$ by $latex \text{quantity} &s=1$, we get

$latex \text{price} = \text{rate} \times \text{quantity} &s=1$.

By multiplying the rate by 1000, we get

Price of 1000 fl oz of deisel in cents $latex = \dfrac{5D}{64}\times 1000 = \dfrac{625D}{8}&s=1$

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