
Concept explainers
a.
To write:
An equation for each person giving the amount of money y the person will donate if you walk x miles.
a.

Answer to Problem 32E
Our complete table would be:
Donor | Amount per mile | Fixed amount | Equation |
Janette | None | $35 | |
Ben | $2 | $20 | |
Salil | $5 | None | |
Mary | $3 | $15 |
Explanation of Solution
Given:
You are participating in a walk-a-thon. Donors can pledge a certain amount of money for each mile that you walk, or a fixed amount that doesn’t depend on how far you walk, or both. The table gives the amounts pledged by four donors on your street:
Donor | Amount per mile | Fixed amount | Equation |
Janette | None | $35 | |
Ben | $2 | $20 | |
Salil | $5 | None | |
Mary | $3 | $15 |
Calculation:
Let x represent number of miles you walk and y represent amount of total money each person will donate.
We can see that Janette only donates fixed amount, so amount of donated by Janette would be
We can see from table that Ben donates $2 per mile and a fixed amount of $20, so amount of donated by Ben would be
We can see that Salil donates $5 per mile and no fixed amount, so amount of donated by Salil would be
Mary donates $3 per mile and a fixed amount of $15, so amount of donated by Mary would be
Therefore, our complete table would be:
Donor | Amount per mile | Fixed amount | Equation |
Janette | None | $35 | |
Ben | $2 | $20 | |
Salil | $5 | None | |
Mary | $3 | $15 |
b.
To write:
An equation giving the total amount of money yyou will raise from the donors on your street, if you walk x miles.
b.

Answer to Problem 32E
Our required equation for total amount of money would be
Explanation of Solution
Given:
You are participating in a walk-a-thon. Donors can pledge a certain amount of money for each mile that you walk, or a fixed amount that doesn’t depend on how far you walk, or both. The table gives the amounts pledged by four donors on your street:
Donor | Amount per mile | Fixed amount | Equation |
Janette | None | $35 | |
Ben | $2 | $20 | |
Salil | $5 | None | |
Mary | $3 | $15 |
Calculation:
The total amount of money ythat you will raise from the donors on your street after walkingx miles will be sum of money donated by each donor as:
Therefore, theequation for total amount of money would be
c.
To consider:
The equations from part (a) and the equation from part (b). Which equation has the graph with the greatest slope? Explain why this is so.
c.

Answer to Problem 32E
The equation from part (b) has the graph with greatest slope.
Explanation of Solution
Given:
You are participating in a walk-a-thon. Donors can pledge a certain amount of money for each mile that you walk, or a fixed amount that doesn’t depend on how far you walk, or both. The table gives the amounts pledged by four donors on your street:
Donor | Amount per mile | Fixed amount | Equation |
Janette | None | $35 | |
Ben | $2 | $20 | |
Salil | $5 | None | |
Mary | $3 | $15 |
Calculation:
Upon looking at equations in part (a) and part (b), we can see that the slope of line in part (b) has a slope of 10. The equations in part (a) has slope of 2, 3 and 5.
Therefore, theequation from part (b) has the graph with greatest slope.
The equations in part (a) represent amount donated by each person. The slope of line in part (b) is greatest because we added all the equations from part (a) to get the total amount of money donated.
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