Algebra I & Mathematics IAlgebra I & Mathematics I

Student EditionStudent Edition

Real Numbers

ISBN 978-1-940836-06-5 — Teacher Edition

ISBN 978-1-940836-05-8 — Student Edition

© 2014

For Information Contact: Center for Mathematics, Science, and Technology 210 W. Mulberry St Illinois State University Normal, IL 61790 309-438-3089 http://cemast.illinoisstate.edu

S T E M Science Technology Engineering Mathematics

Real Numbers

All rights reserved. This file is intended for use by teachers in Illinois only. Any reproduction, or use in any

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Printed in the United States of America.

Real Numbers: Pathways to Common Core Mathematics 61

Reasoning with Equations

Reasoning with Equations

Life is a Highway

Illinois Pathway: Finance

Objective

• Write and solve inequalities.

Materials

• Calculator• Paper/pencil• Job assignment cards with monthly salary

IntroductionAn important part of becoming a teenager is learning how to drive. With driving comes responsibilities and expenses that many teenagers don’t think about. We will explore the costs of gas, insurance, and purchasing a car and how best to budget monthly expenses.

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Student Edition

62 Life is a Highway

Reasoning with Equations

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The teacher will assign you a random monthly income. Incomes range from $350 - $600 per month.

Write your assigned job and income here: _________________________________

One of the largest expenses that you will eventually encounter is transportation. The largest expenses within the transportation budget are gas, insurance, and the cost of a car. Typically, a teen spends no more than 50% of their monthly income on transportation costs (gas, insurance, and cost of a car).

1 Write a simple inequality to show how much of your monthly budget can be allotted towards transportation costs. Use the variable x to represent the most amount of money. Remember, a teen spends no more than 50% of their monthly income on transportation.

2 On average, a teen would spend at most $100 in gas a month. For insurance, a teenage boy would spend $75 per month and a teenage girl would spend $70 per month. You have been assigned the monthly salary from the previous section. Refer back to the salary you were given.

a Write an inequality to represent the amount of money at most you can spend on transportation costs that now include insurance and gas.

b Solve this inequality and determine approximately how much of your 50% budget you have remaining to cover other car expenses.

Real Numbers: Pathways to Common Core Mathematics 63

Chapter 2

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1 What was the inequality you wrote to represent the most amount of money you can spend on total transportation costs based on your monthly salary?

2 What was the inequality you wrote to represent the amount of money you can spend on transportation including gas and insurance?

3 Explain why some drivers may spend more or less money than others?

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Gas prices are always changing. Your budget needs to account for the fact that gas prices may go up from one month to another. In Try It I, you determined how much can be spent from your monthly paycheck on transportation. In this section, you will be writing an inequality to explore gas prices.

1 If you drove to school and home every school day, how many miles would you drive in a month?

2 What is the fuel economy of the vehicle you take to school every day?

3 How many gallons of gasoline will you use every month to travel to and from school?

64 Life is a Highway

Chapter 2

4 Write an inequality with g representing the gas cost per gallon for spending no more than your chosen amount in gas for the month.

5 Solve your inequality for g

6 What is the maximum amount per gallon you can spend and still stay within your 50% budgeted amount?

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1 How many miles/week are you driving to and from school?

2 How many miles/month are you driving to and from school?

3 What was your chosen amount to spend in gas for the month?

4 After solving the inequality from question 4 in the Try It 2 section, is the cost per gallon realistic in today’s market?

Real Numbers: Pathways to Common Core Mathematics 65

Reasoning with Equations

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Using the same monthly salary from the previous sections, you will now determine if you can afford to purchase a car using only a quarter of your monthly salary (25%) to put towards the cost of buying a car.

1 Write a simple inequality to show how much of your monthly budget can be used towards the purchase of a vehicle.

2 Let’s say that you qualify for a 3-year interest free loan. If a loan is interest free, the amount of the loan is divided equally by the number of months that the loan lasts (36 months in this case).

Write an inequality to represent the length of the loan and the amount of money used towards the purchase of a vehicle. Use l to represent the amount of the loan.

3 Choose 3 different types of vehicles found in the local newspaper. Fill in the type of Vehicle and the Sale Price of Car columns with the information you find.

4 Calculate the affordability of that vehicle and if it fits into your monthly budget using the inequality from question 2. Do any of your vehicles fit within your allotted budget of 25%? Explain your reasoning.

66 Life is a Highway

Reasoning with Equations

Car Sale Price of Car Affordable? Yes or No Explain

Vehicle 1:

Vehicle 1:

Vehicle 3:

5 Select a vehicle from the table above that fits into your budget. Including the loan payment, your total transportation costs can now be 75% of your paycheck. Write and solve an inequality to illustrate your fuel costs, your insurance payment, and your car loan payment.

Real Numbers: Pathways to Common Core Mathematics 67

Chapter 2

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Insurance costs can change based on your driving record. The table below shows monthly premiums for teens based on the number of driving infractions incurred.

Driving Record Boys Cost Girls Cost

No infractions $75 $70

1 infraction $100 $85

2 infractions $150 $125

1 major infraction(Texting while driving) $250 $300

1 Use the car you chose in the previous section. The gas amounts, loan amount, and driving distances are the same. The only thing that has changed is your driving record. You have now been issued a speeding ticket. As a result of the speeding ticket, your insurance costs have gone up! Use the table of insurance costs to refigure your transportation costs. Does your car still work in your budget?

Original inequalityNew inequality

(1 infraction)Can you afford this?

Boy

Girl

2 Given all of the same driving parameters from question 1, refigure the affordability if you were ticketed for texting while driving. Can you still afford to own and insure your car?

Original inequalityNew inequality

(1 infraction)Can you afford this?

Boy

Girl

68 Life is a Highway

Chapter 2

Job Assignment Cards

Fast Food Cashier

16 hours/week

$9.25/hour

Gross Income = $592

Net Income = $414

Life Guard/Park District

15 hours/week

$9.00/hour

Gross Income = $540

Net Income = $378

Ice Cream Shop

15 hours/week

$8.50/hour

Gross Income = $510

Net Income = $357

Retail Store

20 hours/week

$9.50/hour

Gross Income = $760

Net Income = $532

Landscaping/Lawn care

20 hours/week

$10.50/ hour

Gross Income $840

Net Income $588

Restaurant

18 hours/week

$4.75/hour + tips

Gross Income = $702

Net Income = $491

Real Numbers: Pathways to Common Core Mathematics 69

Reasoning with Equations

Car Cards

2007 Full-Size Sedan

33 miles/gallon

2005 Sports Sedan

28 miles/gallon

2003 Family Sedan

24 miles/gallon

Mileage Cards

Home to School = 8 milesRoundtrip = 16 miles

Home to School = 10 milesRoundtrip = 20 miles

Home to School = 5 milesRoundtrip = 10 miles