The Situation: Suppose you're catering an event for $200$ guests.
Each guest will get a $6$-fluid-ounce portion of orange juice.
Orange juice concentrate is purchased by the case for $\$22.94.$
Each case contains $12$ cans, and each can makes $0.75$ gallons.
Huge Question #1: How much does one $6$ fluid ounce portion cost?
Huge Question #2: What is the total cost of orange juice for the event?
Huge Answer #1: Find the Cost Per Unit!
First, find how much it costs to prepare one fluid ounce of orange juice.
First, divide the cost by the total number of fluid ounces purchased:
$$CPU=\frac{\$22.94}{\mbox{case}} \frac{1 \mbox{ case}}{12 \mbox{ can}} \cdot \frac{1 \mbox{ can}}{0.75 \mbox{ gal}} \cdot \frac{1 \mbox{ gal}}{128 \mbox{ fl oz}} \approx \frac{\$0.0199}{1 \mbox{ fl oz}}$$
Answer to Huge Question #1
So now if we want to know how much a $6$-fluid ounce portion costs to prepare,
we simply multiply by $1.99$ cents per fluid ounce by $6$ fluid ounces for a total
of $11.94$ cents, or about $12$ cents per $6$-fluid-ounce portion.
Special Note: when calculating cost, we round
up
to the nearest whole cent.
Very Special Note
When doing calculations, it is best to do the entire calculation at once and round off at the end to avoid cumulative
round-off error. When in doubt, use the bridge method:
$$\frac{\$22.94}{12 \mbox{ can}} \cdot \frac{1 \mbox{ can}}{0.75 \mbox{ gal}} \cdot \frac{1 \mbox{ gal}}{128 \mbox{ fl oz}} \cdot 6 \mbox{ fl oz}\approx \$0.1195$$
This is how you need to do it for the homework.
Answer to Huge Question #2
To determine the cost of serving $200$ guests, we multiply the cost per $6$-fluid-ounce portion by $200.$ On paper, and on your
homework, you should do the following calculation:
$$\frac{\$22.94}{12 \mbox{ can}} \cdot \frac{1 \mbox{ can}}{0.75 \mbox{ gal}} \cdot \frac{1 \mbox{ gal}}{128 \mbox{ fl oz}} \cdot 200 \cdot 6 \mbox{ fl oz}\approx \$23.90$$
Reminder: Again, when calculating cost, we round
up
to the nearest whole cent.
General Process: Finding Cost
1) Find the cost per desired unit, or $CPU$, of the food item.
2) Find the amount you will be purchasing in the desired units.
3) You will multiply both quantities obtained in items 1) and 2) above to get
cost.
Use the bridge method to combine these calculations into a single calculation to avoid cumulative round-off error.
Sneak Preview: Calculating total cost can be summarized by the formula
$$\mbox{Cost}=CPU \times APQ.$$
Bonus Example
How much does $2.75$ cups of cocoa powder cost if cocoa powder is purchased in $50$-pound bags for $\$46.30$
and $1$ tablespoon of cocoa powder weighs $0.25$ ounces?
Note: In this case, we will need to use our
weight-volume table
to convert from weight to volume.
Another Bonus Example!
has purchased a kilogram of
Fontina cheese for $\$15.55.$
What is
's cost for $10$ ounces?