Question

Angelo and Deborah are landscapers. Angelo charges $45.50 for eachjob and $15 an hour. Deborah charges $20.50 for each job plus $20 an hour.1. For 2 hours of work, Angelo charges more. T or F?2. For 6 hours of work, Deborah charges more. T or F?3. 45.5x+ 15 = 20.5x + 20 canbe solved to find the numberof hours for which the totalcost is the same to hire eitherlandscaper. T or F?4. Both landscapers charge the same amount for a 5-hour job. T or F?

Answer 1

First, you should convert the text in an equation Math

Now, you have the equations and you should analyze each sentence.

1) For 2 hours of work, Angelo charges more. For analyzing this sentence, you should calculate the total charged by Angelo and Deborah in 2 hours. After that, you should compare the results.

For x=2

Angelo = 45.5 +15x

Angelo = 45.5 +15*2

Angelo = 45.5 +30

Angelo = 75.5

Deborah= 20.5 +20x

Deborah= 20.5 +20*2

Deborah= 20.5 +40

Deborah= 60.5

Angelo > Deborah - True

2)For 6 hours of work, Deborah charges less. For analyzing this sentence, you should calculate the total charged by Angelo and Deborah in 6 hours. After that, you should compare the results.

For x=6

Angelo = 45.5 +15x

Angelo = 45.5 +15*6

Angelo = 45.5 +90

Angelo = 135.5

Deborah= 20.5 +20x

Deborah= 20.5 +20*6

Deborah= 20.5 +120

Deborah= 140.5

Deborah > Angelo - False

3) The equation 45.5x + 15 = 20.5x + 20 can be solved to find the number of hours for which the total cost is the same to hire either landscaper.

The corrected equations are:

Angelo = 45.5 +15x

Deborah= 20.5 +20x

45.5 +15x=20.5 +20x

False

4) Both landscapers charge the same amount for a 5-hour job. For checking this sentence you should equal the equations for Angelo and Deborah and after that, you should use x=5

Angelo = 45.5 +15x

Deborah= 20.5 +20x

45.5 +15x=20.5 +20x

45.5 +15*5=20.5 +20*5

45.5+75=20.5+100

120.5=120.5

True