Chapter 3, Problem 26CT

To determine

To find the number of whole loaves bread must be made so that the cost of the machine and the ingredient will be less than the cost of buying an equivalent amount of bread from the store.

Answer to Problem 26CT

57 loaves of bread must be made so that the cost of the machine and the ingredient will be less than the cost of buying an equivalent amount of bread from the store.

Explanation of Solution

Given information:

A bread- making machine costs $99.

The ingredients to make a one pound loaf of bread cost $0.45.

At a store, you pay $2.16 for the same size of bread.

Calculation:

Let $ $x$ be the whole loaf of bread to make.

Therefore,

  $\begin{array}{l}\text{Cost of machine}+\text{cost of ingredients to make one pound bread}\times \text{Number of breads to make}\\ <\text{Cost of one bread}\times \text{Number of bread }\end{array}$

Substitute the values in above statement and solve:

  $\begin{array}{l}99+0.45x<2.19x\text{ (Substitute)}\\ 99+0.45x-0.45x<2.19x-0.45x\text{ (Subtract }0.45x\text{ from each side)}\\ 99<1.74x\text{ (Simplify)}\\ \frac{99}{1.74}<\frac{1.74x}{1.74}\text{ (Divide each side by 1}\text{.74)}\\ 56.89<x\text{ (Simplify)}\end{array}$

Hence,

57 loaves of bread will you have to make.