1. ## unit conversion

I can't seem to figure this one out. Can someone explain?

The price of ground coffee beans is d dollars for 8 ounces and each ounce makes c cups of brewed coffee. In terms of c and d, what is the dollar cost of the gound coffee beans required to make 1 cup of brewed coffee?

A) $\displaystyle \dfrac{d}{8c}$

B) $\displaystyle \dfrac{cd}{8}$

C) $\displaystyle \dfrac{8c}{d}$

D) $\displaystyle \dfrac{8d}{c}$

E) $\displaystyle 8cd$

2. In these kind of problems, it is best to set up ratios and you have to be careful with your units.

Price of ground coffee beans: $\displaystyle \frac{d\ \text{dol}}{8\ \text{oz}}$

Ratio of ounces to cups: $\displaystyle \frac{1\ \text{oz}}{c\ \text{cups}}$

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Now I need to find the cost of the ground coffee beans required to make 1 cup of brewed coffee. So, what we do first, is convert 1 cup into oz using the ratio given:

$\displaystyle \frac{1\ \text{oz}}{c\ \text{cups}} \cdot 1\ \text{cup}$

Notice that the cup unit cancel (and don't leave the s behind! ):

$\displaystyle \frac{1\ \text{oz}}{c\ \text{\rlap{////}{cups}}} \cdot 1 \text{\rlap{///}{cup}}$

$\displaystyle = \frac{1\ \text{oz}}{c}$

Now, last thing to do is to multiply the converted unit with the price:
$\displaystyle \frac{d\ \text{dol}}{8\ \text{oz}} \cdot \frac{1\ \text{oz}}{c}$

Again, the units cancel, leaving you with the price:
$\displaystyle \frac{d\ \text{dol}}{8\ \rlap{//}{\text{oz}}} \cdot \frac{1\ \rlap{//}\text{oz}}{c}$

$\displaystyle = \frac{d}{8c}\ \text{dol}$

3. Ah, I see it thank you!