Summer Jobs: Compare the Pay

Use graphs, tables, and equations to compare mowing and babysitting rates.

Read the Mowing Graph

Amira mows lawns during the summer. Her earnings are proportional to her working time. On the graph, each vertical unit represents $10.

What does point P represent?

A. Amira earns $4 for 2 hours of mowing.B. Amira earns $40 for 2 hours of mowing.C. Amira earns $2 for 4 hours of mowing.D. Amira earns $20 for 4 hours of mowing.

Find the slope of the mowing graph in its displayed units. Then express the hourly pay in dollars.

Slope = tens of dollars per hour.
Hourly pay = $ per hour.

Let x be hours of mowing and y be earnings in dollars, not tens of dollars. Which equation models Amira's pay?

A. y = 20xB. y = 20 + xC. y = 2xD. y = x/20

Amira can accept a mowing job that pays $70 at her usual hourly rate. Use the proportional relationship to find the working time.

The job takes hours.

Compare Job Offers

Amira also babysits. Her usual babysitting pay is shown below. All pay in this section is proportional to working time, with no extra fees or bonuses.

Usual Babysitting Pay
Time (hours)	Earnings (dollars)
1.5	18
3	36
4.5	54

Suppose both usual job rates are graphed with hours horizontally and dollars vertically on the same axes. Which statement is correct?

A. The babysitting line is steeper because its rate is $12 per hour greater.B. The mowing line is steeper because its rate is $2 per hour greater.C. The mowing line is steeper because its rate is $8 per hour greater.D. The babysitting line is steeper because its rate is $36 per hour.

Graph the usual babysitting relationship on these axes. Each vertical unit represents $10. Plot the origin and the point for 5 hours, then draw a straight line segment between them.

Amira chooses between 2 hours of mowing and 3 hours of babysitting at her usual rates. The mowing job pays more, even though it takes less time.

How much more does the mowing job pay? $

Amira receives four new offers. Select every offer whose hourly rate would produce a steeper earnings graph than her usual mowing rate of $20 per hour. Compare using hours and dollars on identical axes.

A family raises Amira's babysitting rate from $12 to $18 per hour. If the axes stay the same, how does the slope of her earnings graph change?

A. The new slope is 2/3 of the original slope.B. The new slope is 6 times the original slope.C. The new slope is 1/2 of the original slope.D. The new slope is 1.5 times the original slope.

Check the Summer Schedule

Use unit rates to make each comparison. Unless a question gives a new rate, mowing pays $20 per hour and babysitting pays $12 per hour.

10.

A neighbor offers $27 for each lawn. Each lawn takes Amira 1.5 hours, and this rate stays constant. Compare this offer's hourly rate with her usual babysitting rate.

The neighbor's hourly mowing rate is times her usual babysitting rate.

11.

A new babysitting offer pays $14 per hour plus a one-time $6 bonus. Amira wants to graph total pay against hours. Why is this offer not a proportional relationship?

A. Its graph passes through (0, 6), not the origin.B. Its graph rises by $6 for every hour worked.C. Its graph has a different slope at every point.D. Its graph passes through (0, 14), not the origin.

12.

In each equation, x is hours and y is earnings in dollars. Select every proportional pay model with a rate strictly between Amira's usual babysitting and mowing rates.

13.

Amira plans to work 3 hours mowing and 2 hours babysitting at her usual rates. Instead, she could spend all 5 hours mowing. Compare the total earnings of these schedules.

Working all 5 hours mowing would earn $ more.

14.

Leo finds a slope of 2 on Amira's mowing graph, where earnings are in tens of dollars. He finds a slope of 12 for her babysitting table, where earnings are in dollars. He says, “Babysitting pays more because 12 is greater than 2.” Explain the problem with comparing these slopes directly. Compare the pay rates using matching units.