1. Anna and Jason have summer jobs stuffing envelopes for two different companies. Anna earns $14 for every 400 envelops she fin
ishes. Jason earns $9 for every 300 envelopes he finishes.
A. Draw graphs and write equations that show the earnings, y as functions of the number of envelopes stuffed, n for Anna and Jason. (You will have to create your own coordinate plane)
B. Who makes more from stuffing the same number of envelopes? How can you tell this from the graph?
C. Suppose Anna has savings of $100 at the beginning of the summer and she saves all her earnings from her job. Graph her savings as a function of the number of envelopes she stuffed, n. How does this graph compare to her previous earnings graph? What is the meaning of the slope in each case?
A. Draw graphs and write equations that show the earnings, y as functions of the number of envelopes stuffed, n for Anna and Jason. (You will have to create your own coordinate plane)
B. Who makes more from stuffing the same number of envelopes? How can you tell this from the graph?
C. Suppose Anna has savings of $100 at the beginning of the summer and she saves all her earnings from her job. Graph her savings as a function of the number of envelopes she stuffed, n. How does this graph compare to her previous earnings graph? What is the meaning of the slope in each case?
1 answer:
The amount of money earned, y, and the number of envelopes stuffed, n, are proportional to each other. Since Anna earns $14 for 400 envelopes, she makes 14400=0.035n for Anna's equation. Jason earns $9 for every 3000 envelopes he stuffs, so he makes 9300=0.03 dollars per envelope. So we have y=0.03 for Jason's equation.
Since Anna's equation has a larger unit rate, 0.035 dollars per envelope vs. 0.03 dollars per envelope for Jason, she has the higher paying job.
A useful graph will be shown below. Which I hope will help you more.
A.) For every envelope they stuff, Anna makes half a cent more than Jason. Since Anna makes more money per envelope, her earnings increase faster than Jason's Therefore, here earnings lines is steeper than Jason's.
B.) Anna still earns money at the same rate as before, but not her earnings are added to her savings of $100. The graph showing her total savings, including the money she earns, is still linear but it has a higher starting value. The new line is parallel to the previous earnings line but while the previous line went through the point (0,0), the new line starts at the point (0,100). This shows that when she starts working she already has $100 in savings.
For her earnings graph, we see that she will make $0.035 for every envelope she stuffs, but for her savings, she will save an additional$0.035 for every additional envelope she stuffs.
Since Anna's equation has a larger unit rate, 0.035 dollars per envelope vs. 0.03 dollars per envelope for Jason, she has the higher paying job.
A useful graph will be shown below. Which I hope will help you more.
A.) For every envelope they stuff, Anna makes half a cent more than Jason. Since Anna makes more money per envelope, her earnings increase faster than Jason's Therefore, here earnings lines is steeper than Jason's.
B.) Anna still earns money at the same rate as before, but not her earnings are added to her savings of $100. The graph showing her total savings, including the money she earns, is still linear but it has a higher starting value. The new line is parallel to the previous earnings line but while the previous line went through the point (0,0), the new line starts at the point (0,100). This shows that when she starts working she already has $100 in savings.
For her earnings graph, we see that she will make $0.035 for every envelope she stuffs, but for her savings, she will save an additional$0.035 for every additional envelope she stuffs.
You might be interested in