Chapter 6.1, Problem 40E

To determine

To calculate:The size of cup which costs least per ounce.

Answer to Problem 40E

The small cup costs the least per ounce.

Explanation of Solution

Given information:

The small cup costs $\$0.89$ and holds $9$ ounces.

The medium cup costs $\$1.29$ and holds $12$ ounces.

The large cup costs $\$1.59$ and holds $15$ ounces.

Calculation:

To determine the size of cup that costs least per ounce, calculate the cost of each cup per ounce. To do so, find the unit rate.

For the small cup, unit rate is:

  $\begin{array}{l}\frac{\$0.89÷9}{9\text{ ounces}÷9}\text{ [Divide numerator and denominator by }9\text{]}\\ \Rightarrow \frac{\$0.099}{1\text{ ounce}}\end{array}$

Therefore, the cost is $\$0.099$ per ounce for the small cup.

For the medium cup, unit rate is:

  $\begin{array}{l}\frac{\$1.29÷12}{\text{12 ounces}÷12}\text{ [Divide numerator and denominator by 12]}\\ \Rightarrow \frac{\$0.108}{1\text{ ounce}}\end{array}$

Therefore, the cost is $\$0.108$ per ounce for the medium cup.

For the large cup, unit rate is:

  $\begin{array}{l}\frac{\$1.59÷15}{\text{15 ounces}÷15} \text{[Divide numerator and denominator by 15]}\\ \Rightarrow \frac{\$0.106}{1\text{ ounce}}\end{array}$

Therefore, the cost is $\$0.106$ per ounce for the large cup.

Conclusion: Since among the three, $\$0.099$ per ounce is the least cost the, the small cup costs the least.