Question

I. The Bread Machine (25 points)
In real life, you must often make choices about whether to buy something pre-made or make it yourself. There are many things to consider: quality of homemade vs. bought, expense, convenience, enjoyment of making something, etc. In this response, you will be looking at the choice of buying a bread machine or relying exclusively on store bought bread.

A. The bread machine you are interested in costs $100 with tax.
The ingredients to make one loaf of bread cost $0.80.
What is the rate of cost of one loaf of bread?


B. What is your start up cost? (cost of machine)


C. Write a linear equation, y = mx + b for the total cost.

E. A loaf of bread of similar quality in the store costs $1.60. This is the rate for a loaf of bread (the slope). As there is no other cost, your beginning point (y-intercept) is zero. Write the linear equation y = mx + b for the total cost.


F. Graph the equation on the same graph you used in D. You may use either Point Plotting or Slope-Intercept. Be sure to locate at least 3 points. You may want to do this in pencil in case you decide to use more points later in the problem.

G. Estimate the ordered pair where the two lines cross and write it here: (______, ______)

H. The x-value where they cross represents the number of loaves it will take to make the costs of the bread machine and buying the bread equal and the y-value represents the cost where they are the same. Fill in:

It would take _________ loaves at a cost of $_________ for the breadmaker and store bought bread to cost the same.

Answer 1

It would take 125 loaves at a cost of $200 for the breadmaker and store bought bread to cost the same.

Linear equation

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept.

Let x represent the rate of cost of one loaf and y represent the total cost, hence:

y = 0.8x + 100

The rate of cost of one loaf is $0.8 and the start up cost is $100.

For the second bread it is given by:

y = 1.6x

The graph of the two equations cross at (125, 200)

It would take 125 loaves at a cost of $200 for the breadmaker and store bought bread to cost the same.

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