Chapter 8, Problem 5PSP

To determine

To find:

3 possible combinations of pies and loaves of bread you can make that use up all the pumpkin.

Answer to Problem 5PSP

3 possible combinations would be 2 pies and 9 loaves of bread, or 4 pies and 6 loaves of bread, or 6 pies and 3 loaves of bread.

Explanation of Solution

Given:

You have 12 cups of fresh pumpkin to use for baking. You need $1\frac{1}{2}$ cups to make a pumpkin pie and 1 cup to make a loaf of pumpkin bread.

Calculation:

Let x represent number of pies and y represent number of loaves of bread.

We have been given that we need $1\frac{1}{2}$ cups to make a pumpkin pie, so cups of pumpkin needed for xpies would be $1\frac{1}{2}x=1.5x$ .

We have been given that we need 1 cup to make a loaf of bread, so cups of pumpkin needed for ybread loaves would be $y$ .

The total amount of pumpkin needed would be $1.5x+y$ .

Since we have 12 cups of fresh pumpkin to use, so we will equate $1.5x+y$ with 12 as:

  $1.5x+y=12$

Now we substitute some values of x and solve for y as:

  $\begin{array}{l}1.5x+y=12\left(\text{Our equation }\right)\\ 1.5(2)+y=12\left(\text{Substituting }x=2\right)\\ 3+y=12\\ 3-3+y=12-3\\ y=9\end{array}$

  $\begin{array}{l}1.5x+y=12\left(\text{Our equation }\right)\\ 1.5(4)+y=12\left(\text{Substituting }x=4\right)\\ 6+y=12\\ 6-6+y=12-6\\ y=6\end{array}$

  $\begin{array}{l}1.5x+y=12\left(\text{Our equation }\right)\\ 1.5(6)+y=12\left(\text{Substituting }x=6\right)\\ 9+y=12\\ 9-9+y=12-9\\ y=3\end{array}$

Therefore, 3 possible combinations would be 2 pies and 9 loaves of bread, or 4 pies and 6 loaves of bread, or 6 pies and 3 loaves of bread.