1. Your math class is selling candy bars for a fundraiser. Each bar costs $3. Your class already has $150 in its account. The goal is to have a total of $237 after the fundraiser in the account.

a. Make a table, graph and write a rule showing the total money in your class account.

b. How many candy bars would it take to reach the goal?

c. How much money would your class have total if they sold 14 candy bars (use a different method than part b)?

We can call x the number of candy bars sold. The linear equation for the fund can be represented by y=150+3x dollars (this is the rule). That's the initial amount of $150 plus $3 for each candy bar. When y=$237, the goal, 237=150+3x, so 3x=237-150=87 and x=87/3=29 to meet the goal. A graph of y=150+3x can be drawn where 150 is the y intercept and -50 is the x intercept. By joining these intercepts and continuing to the right you will see a graph showing values of x and corresponding values of y on the graph to the right. The graph can be drawn near the bottom of the page to allow y to extend to about 240 with suitable scaling. The only reason to draw the graph away from the left of the page is to accommodate x=-50, the x intercept. The only meaningful part of the graph is to the right of the y axis and above the x axis, the positive region for both x and y. If you read off the x value for y=237 you should see that it's 29. You can also see what value of y corresponds to x=14. It should be y=192. A comfortable scaling for both axes is tenth of an inch for each unit, so 80 units on the x axis is 8" and 240 units on the y axis is 2 feet (a long sheet of paper!). To shorten the y axis, you can take y from 150 to 240, 90 units, or 9". That means losing 5" on the x axis so that x starts at 0 and goes up to about 30 or 3". You don't need the same scale on each axis, so you could divide the y axis so that 1/10=2 units, making the y axis 12" instead of 24". Play around with the scaling and show your daughter what you are doing. To make a table of x and y values, for example:

x y

0 150

10 180

20 210

30 240

Join these points to get the line and choose the scale that gives you the best readings.

I hope this helps you both.

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