Question

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:

Problem 17

Part a

Step1: Define variables

Let \( x \) be the number of digital images, and \( C \) be the total cost in dollars.

Step2: Determine fixed and variable costs

The sitting fee is a fixed cost of $150, and each digital image costs $15 (variable cost). A linear model has the form \( C = mx + b \), where \( m \) is the slope (variable cost per unit) and \( b \) is the y - intercept (fixed cost). Here, \( m = 15 \) and \( b = 150 \).

Step3: Write the linear model

So the linear model is \( C=15x + 150 \).

Step1: For \( x = 0 \)

Substitute \( x = 0 \) into \( C = 15x+150 \). Then \( C=15(0)+150=150 \).

Step2: For \( x = 2 \)

Substitute \( x = 2 \) into \( C = 15x + 150 \). \( C=15(2)+150=30 + 150=180 \).

Step3: For \( x = 4 \)

Substitute \( x = 4 \) into \( C = 15x+150 \). \( C=15(4)+150=60 + 150=210 \).

Step4: For \( x = 6 \)

Substitute \( x = 6 \) into \( C = 15x+150 \). \( C=15(6)+150=90+150 = 240 \).

Step5: For \( x = 10 \)

Substitute \( x = 10 \) into \( C = 15x+150 \). \( C=15(10)+150=150 + 150=300 \).

Step1: Define variables

Let \( x \) be the number of miles driven, and \( C \) be the total charge in dollars.

Step2: Determine fixed and variable costs

The rental fee is a fixed cost of $75, and the cost per mile is $0.15 (variable cost). Using the linear model \( C=mx + b \), where \( m = 0.15 \) and \( b = 75 \).

Step3: Write the equation

The equation is \( C=0.15x + 75 \).

Answer:

\( C = 15x+150 \)

Part b