Applications

Site:	Harrison
Course:	Michigan Algebra I Sept. 2012
Book:	Applications

Printed by:	Guest user
Date:	Sunday, 24 November 2024, 12:15 AM

Description

Problem 1
- Answer 1
Problem 2
- Answer 2
Problem 3
- Answer 3
Problem 4
- Answer 4
Problem 5
- Answer 5
Practice
- Answer Key
Sources

Problem 1

Marcel rented a moving truck for the day. Marcel remembers that the rental truck company charges $40 per day, but has forgotten how many cents per mile he is charged. Marcel drives 46 miles and the final amount of the bill (before tax) is $63. What is the amount per mile the truck rental company charges? Write an equation in point-slope form that describes this situation. How much would it cost to rent this truck if Marcel drove 220 miles?

Answer 1

Step 1. Define the variables.

x = distance in miles
y = cost of the rental truck in dollars

Step 2. Determine the y-intercept and a point.

The y-intercept is given, the cost of the truck with 0 miles is $40 so the y-intercept is (0, 40).

Marcel pays $63 for 46 miles, representing the point (46, 63).

Step 3. Use the y-intercept (b) and the given point (x, y) to determine the function rule.

App1

Step 4. Substitute values for m and a point into

Step 5. To answer the question about the cost of 220 miles, substitute x = 220.

Listen

Problem 2

Anne got a job selling window shades. She receives a monthly base salary and a $6 commission for each window shade she sells. At the end of the month, she adds up her sales and she figures out that she sold 200 window shades. She made $2500. Write an equation in point-slope form that describes this situation. How much is Anne's monthly base salary?

Answer 2

Step 1. Define the variables.

x = number of window shades sold
y = Anne's monthly salary in dollars

Step 2. Determine the slope and a point.

Anne gets $6 for each shade, so the slope = 6 dollars/shade.
She sold 200 shades and made $2500, representing the point (200, 2500).

Step 3. Determine the function rule by using the point-slope form.

Step 4. Determine Anne's base salary by substituting x = 0.

App2-2

$1300 is Anne's base salary.

Listen

Problem 3

Nadia has $200 in her savings account. She gets a job that pays $7.50 per hour and she deposits all her earnings in her savings account. Write the equation describing this problem in slope-intercept form. How many hours would Nadia need to work to have $500 in her account?

Answer 3

Step 1. Define the variables.

y = amount of money in Nadia's savings account
x = number of hours

Step 2. Determine the y-intercept and slope.

Nadia has $200 in her savings account, so b = 200.

She has a job that pays $7.50 per hour, so m = 7.50.

Step 3. Determine the function rule using the slope-intercept form.

y = 7.5x + 200

Step 4. Substitute and solve to determine the number of hours Nadia needs to work to earn $500.

500 = 7.5x + 200
7.5x = 300
x = 40

Nadia needs to work 40 hours to earn $500.

Listen

Problem 4

Nimitha buys fruit at her local farmer's market. This Saturday, oranges cost $2 per pound and cherries cost $3 per pound. She has $12 to spend on fruit. Write an equation in standard form that describes this situation. If she buys 4 pounds of oranges, how many pounds of cherries can she buy?

Answer 4

Step 1. Define the variables.

x = pounds of oranges
y = pounds of cherries

Step 2. Write an equation.

Since there are two rates, neither can be the slope alone.
Therefore, the equation that describes this situation is: 2x + 3y = 12

Step 3. Substitute 4 for x and solve for y.

App4-1

Nimitha can buy pounds of cherries.

Listen

Problem 5

Jethro skateboards part of the way to school and walks for the rest of the way. He can skateboard at 7 miles per hour and he can walk at 3 miles per hour. The distance to school is 6 miles. Write an equation that describes this situation. If Jethro skateboards for half an hour, how long does he need to walk to get to school?