Chapter 6.2, Problem 50E

To determine

To find the box of pasta having a low price and the money saved in buying $\text{6 pounds}$ of pasta from the box having a lower price.

Answer to Problem 50E

  $\text{2 pound}$ box has lower price per ounce.

  $\$1.72$ will be saved in buying the pasta from the $\text{2 pound}$ box.

Explanation of Solution

Given information:

A $\text{12 ounce}$ box of pasta costs $\$.99$ and a $\text{2 pound}$ box costs $\text{\$2}\text{.09}$ .

Calculation :

The cost of one ounce pasta from the $\text{12 ounce}$ box can be calculated by:

  $\begin{array}{l}\text{Cost of 12 ounces of pasta=\$}\text{.99}\\ \text{Cost of 1 ounce of pasta=}\frac{\text{\$}\text{.99}}{12}\\ \text{ Cost of 1 ounce of pasta}=\$0.083\end{array}$

The cost of one ounce of pasta from the $\text{2 pound}$ box can be calculated by:

  $\begin{array}{l}\text{Cost of 2 pounds of pasta}=\$2.09\\ \text{Cost of 32 ounces of pasta}=\$2.09\left[\text{1 pound=16 ounce}\right]\\ \text{Cost of 1 ounce of pasta=}\frac{\text{\$2}\text{.09}}{32}\\ \text{Cost of 1 ounce of pasta=\$0}\text{.065 }\end{array}$

Hence, $\text{2 pound}$ box has lower price per ounce.

  $\text{6 pound}$ pasta should be bought from the $\text{2 pound}$ box.

The money saved in buying the pasta from the $\text{2 pound}$ box can be calculated by:

  $\begin{array}{l}\text{Cost of buying 6 pounds pasta from the 12 ounce box}=\$\left(0.083\times 96\right)\left[\begin{array}{l}\text{Multiplying the cost of 1 ounce by 96, }\\ \text{6 pounds=96 ounce}\end{array}\right]\\ \text{Cost of buying 6 pounds pasta from the 12 ounce box}=\$7.96\\ \text{Cost of buying 6 pounds pasta from the 2 pound box}=\$\left(0.065\times 96\right)\left[\begin{array}{l}\text{Multiplying the cost of 1 ounce by 96, }\\ \text{6 pounds=96 ounce}\end{array}\right]\\ \text{Cost of buying 6 pounds pasta from the 2 pound box}=\$6.24\\ \text{Money saved in buying pasta from the 2 pound box}=\$\left(7.96-6.24\right)\\ \text{Money saved in buying pasta from the 2 pound box}=\$1.72\end{array}$

Hence, $\$1.72$ will be saved in buying the pasta from the $\text{2 pound}$ box.