1. Using Graphs to Relate Two Quantities
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Make a table to determine the cost based on the number of shirts purchased.
The cost of the first 5 shirts is 12.99 per shirt. Each shirt after the fifth costs 4.99. The total cost depends on the number of shirts purchased. This is reflected by the following graph.
For this exercise, it seems the person who drew the graph misunderstood the given situation. First of all, if you do not buy any shirts, the cost is 0 so the graph should start from the origin. Also, it is given that the first five shirts cost $12.99 each. This means we would add 12.99 to our total cost for each shirt purchased.
| Number of shirts purchased (n) | 12.99n | Cost |
|---|---|---|
| 0 | 12.99 * 0 | 0 |
| 1 | 12.99 * 1 | 12.99 |
| 2 | 12.99 * 2 | 25.98 |
| 3 | 12.99 * 3 | 38.97 |
| 4 | 12.99 * 4 | 51.96 |
| 5 | 12.99 * 5 | 64.95 |
The table above shows that we should see a constant increase between 0 and 5 shirts. The given graph does not coincide with this as it shows a horizontal line. It is likely that the person interpreted this part of the situation to be "5 shirts cost 12.99." At this point, we have the following graph.
Each shirt after the fifth costs 4.99 each. This means that we have to add 4.99 to the cost of the first five shirts every time we purchase another shirt. This is shown in the table below.
| Number of shirts purchased (n) | 4.99(n-5) + 64.95 | Cost |
|---|---|---|
| 5 | 4.99( 5-5) + 64.95 | 64.95 |
| 6 | 4.99( 6-5) + 64.95 | 69.94 |
| 7 | 4.99( 7-5) + 64.95 | 74.93 |
| 8 | 4.99( 8-5) + 64.95 | 79.92 |
| 9 | 4.99( 9-5) + 64.95 | 84.91 |
Again, the given graph does not coincide with this piece of information. The vertical drop in the given graph shows a decrease in price from 5.99 to 4.99, but the y-axis is supposed to reflect the total cost of the shirts so it should increase but at a slower rate.
