Question

14.
15.

1. a cell phone company charges $50 a month for phone service and an additional $0.05 per text message.

a. write an equation to model the total charge, y (in dollars) in terms of x, the number of texts sent.
b. use the equation you found to complete the table.

texts	25	50	100	200

1. a photographer charges $150 for a sitting fee. digital images cost $15 each.

a. write a linear model that gives the total cost in dollars in terms of how many digital images you purchase.
b. use the equation to complete the table.

digital images	0	2	4	6	10

1. a car rental company charges a $75 rental fee and an additional $0.15 per mile.

a. write an equation to model the total charge in terms of the number of miles driven.
b. find the cost of renting a car for 50 miles.
c. find the number of miles you can drive if you have $135 to spend.

Explanation:

16b Solution:

Step1: For \( x = 100 \)

Use the equation \( y = 0.05x + 50 \). Substitute \( x = 100 \):
\( y = 0.05(100) + 50 = 5 + 50 = 55 \)

Step2: For \( x = 200 \)

Substitute \( x = 200 \) into \( y = 0.05x + 50 \):
\( y = 0.05(200) + 50 = 10 + 50 = 60 \)

Let \( x \) = number of digital images, \( y \) = total cost.
Fixed cost = $150$, variable cost = $15x$.
Thus, the linear model is \( y = 15x + 150 \).

Step1: \( x = 0 \)

Substitute \( x = 0 \) into \( y = 15x + 150 \):
\( y = 15(0) + 150 = 150 \)

Step2: \( x = 2 \)

Substitute \( x = 2 \):
\( y = 15(2) + 150 = 30 + 150 = 180 \)

Step3: \( x = 4 \)

Substitute \( x = 4 \):
\( y = 15(4) + 150 = 60 + 150 = 210 \)

Step4: \( x = 6 \)

Substitute \( x = 6 \):
\( y = 15(6) + 150 = 90 + 150 = 240 \)

Step5: \( x = 10 \)

Substitute \( x = 10 \):
\( y = 15(10) + 150 = 150 + 150 = 300 \)

Answer:

Texts	25	50	100	200

17a & 17b Solution:

17a: