ERIE COMMUNITY COLLEGE
TITLE III
Linear Equations Project
Interdisciplinary Course Materials
Allied Health
Course:
MT 007 (College Elementary Algebra II) or MT 013 (College Elementary Algebra)
Course Outline Topics:
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Perform fundamental operations (addition, subtraction, multiplication, division) with real numbers.
Evaluate formulas, solve linear equations, linear inequalities, and ratio proportion problems.
Demonstrate a sense of numbers by determining if a mathematical solution is “reasonable”.
Present organized written work.
Read critically and think logically when solving application problems.
Demonstrate an understanding of order of operations to complete calculations on a scientific calculator.
Solve systems of linear equations by graphing, addition and substitution methods.
Present organized written work and show a check to avoid careless mistakes.
Project Title: Exercise, Calories and Systems of Equations
Project Description:
Students will use an Exercise Calorie Expenditure table to obtain 30 minute calorie equivalents for varying
exercises. These will be used to solve systems of equations relating weight, time spent exercising and calories
burned. Checks will be required for all work.
Author:
Lynette Meslinsky, Mathematics/Computer Science
Curriculum Expert: Jill O’Malley, Biology
Semester Created: Fall 2008
A. Essential Question (What does this project attempt to answer?)
How can I use systems of equations to solve problems relating calories and time spent exercising?
B. Introduction:
A table has been provided for you to use with this project which provides data for different weights on Exercise
Calorie Expenditures Sorted by Activity. This table gives you an idea of how many calories you may be
expending while performing a range of activities for 30 minutes. Each column shows the estimated calories for
the specified body weight. You may interpolate values if your body weight falls between two of these values.
If you are not familiar with interpolation, you many round your weight to the nearest category.
Erie Community College
Title III Grant
C.
Things to Learn Before Starting the Project
Before you begin this project you will need to know how to solve a system of equations using algebraic
techniques taught in class. You will also need to know how to interpret the Exercise Calorie Expenditure Table
included with the project. Finally you will need to know how to use your scientific calculator to perform the
mathematical operations needed in your solution.
D & E. Directions & Project Assignment:
Each problem below can be solved by using a system of linear equations. Enter the data you will need for each
problem by referring to the Exercise Calorie Expenditure Table included with the project. Use variables for
unknown quantities. Write the system of equations you will use for each problem and solve using one of the
algebraic techniques you have learned in class (either Substitution or Addition). Round your answers to the
nearest hundredth where necessary. Show a check for your solution to the problem.
Problem 1:
Sue weighs 150 pounds and is trying to lose weight before her sister’s wedding. She would like to lose one pound per
week (3500 calories burned) and has started going to the gym. Each week she goes to 2 one hour aerobic step classes.
a) How many hours will she need to spend on the Stair Climber each week to achieve her goal of burning 3500
calories?
b) What is the total number of hours Sue will spend exercising each week?
c) Show a check for you work.
Activity Calories Burned per Hour Number of Hours Total Calories Burned
Problem 2:
The weather has gotten nicer and Sue is tired of going to the gym. She would rather exercise outside by riding her bicycle
(10 mph) and walking (4 mph). She only has time to fit in 10 hours of exercise with her busy schedule.
a. How much time should she spend doing each of the fitness activities?
b. Show your check.
Activity Calories Burned per Hour Number of Hours Total Calories Burned
Erie Community College
Title III Grant
Problem 3
Bob has had a busy week but has still found time for playing basketball even though there has been quite a lot of snow
and he has had to work at shoveling his driveway. He weighs 190 pounds and has burned 4781 calories with these two
activities.
a. If his total time spent shoveling and playing basketball is 6 hours, find out how much time he spent doing each.
b. Convert your answers to hours and minutes.
c. If 3500 calories burned is equal to one pound of weight loss, how many pounds has Bob burned off?
Activity Calories Burned per Hour Number of Hours Total Calories Burned
Problem 4:
Marcus spends his free time by Weight Training at the gym (60 second intervals) and hiking (with no load) in the
woods near his home. One week he burned 4760 calories by hiking for 4 hours and weight training for 3. The next week
he burned 5000 calories by hiking for 5 hours and weight training for 2.5 hours.
a. Find the calories burned for each activity.
b. Use the table to determine how much Marcus weighs.
c. Show a check for your work.
Activity Calories Burned per Hour Number of Hours Total Calories Burned
Week 1 Week 2 Week 1
Week 2
Erie Community College
Title III Grant
F.
Student Resources
Students will need a scientific calculator and Calorie Expenditure Table. If they would like more information
on activity and calories they can visit the website:
www.nutribase.com/exercala.htm
G.
Faculty Resources
Students will need to have developed the procedural knowledge necessary to manipulate formulas and
equations. In addition they will need instruction in the use of a scientific calculator to execute the mathematical
operations needed to solve the systems of equations. You will need to have covered systems of equations and
their applications before assigning this project.
H.
Scoring Rubric
All parts should be graded on Mathematical logic used through work shown (50%) as well as accuracy (50%)
Each problem (1 – 4) is worth 25%.
Erie Community College
Title III Grant