To babysit one child, fernando charges $10 to drive to the appointment plus $4 per hour. he saves 30% of the total amount he earns. brenna charges $6 per hour and saves 25% of the total amount she earns. which equation can be used to determine the number of hours, h, after which fernando and brenna will have saved the same amount of money?

10 hours

Explanation:

1) Fernando's earnings:

10 + 4h ← 10 is a fix charge, h is the number of hours and 4 is the rate per hour

2) Fernando's savings

0.30 (10 + 4h) ← 30% = 30 / 100 = 0.3

3 + 1.2h ← distributive property

3) Brenna's earnings

6h ← h is the number of hours, 6 is the rate per hour

4) Brenna's savings

0.25(6h) ← 25% = 25/100 = 0.25

1.5h ←0.25 × 6 = 1.5

5) Equal savings

3 + 1.2h = 1.5h

1.5th- 1.2h = 3 ← transpose terms

0.3h = 3 ← combine like terms

h = 3 / 0.3 = 10 ← divide by 0.3

h = 10

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.