Chapter 8.5, Problem 32E

a.

To determine

To write:

An equation for each person giving the amount of money y the person will donate if you walk x miles.

Answer to Problem 32E

Our complete table would be:

Donor	Amount per mile	Fixed amount	Equation
Janette	None	$35	$y=35$
Ben	$2	$20	$y=2x+20$
Salil	$5	None	$y=5x$
Mary	$3	$15	$y=3x+15$

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 $y=35$ .

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 $y=2x+20$ .

We can see that Salil donates $5 per mile and no fixed amount, so amount of donated by Salil would be $y=5x$ .

Mary donates $3 per mile and a fixed amount of $15, so amount of donated by Mary would be $y=3x+15$ .

Therefore, our complete table would be:

Donor	Amount per mile	Fixed amount	Equation
Janette	None	$35	$y=35$
Ben	$2	$20	$y=2x+20$
Salil	$5	None	$y=5x$
Mary	$3	$15	$y=3x+15$

b.

To determine

To write:

An equation giving the total amount of money yyou will raise from the donors on your street, if you walk x miles.

Answer to Problem 32E

Our required equation for total amount of money would be $y=10x+70$ .

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:

  $\begin{array}{l}y=35+2x+20+5x+3x+15\\ y=2x+5x+3x+20+35+15\\ y=10x+70\end{array}$ .

Therefore, theequation for total amount of money would be $y=10x+70$ .

c.

To determine

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.

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.