Learning Objectives
Introduction
In this tutorial we will be solving problems using formulas to help us. In Tutorial 8: An Introduction to Problem Solving, we had to create our own equations based on the given information. However, all of the problems we will be solving in this tutorial will involve using a formula to get to our final answer. We will be looking at such formulas as compound interest, distance/rate, volume of a sphere, and so on. Since we are still problem solving, I will use Polya’s four steps to Problem Solving as introduced in Tutorial 8: An Introduction to Problem Solving to step us through the word problems in this tutorial. After going through this tutorial, you will be an old pro at solving word problems involving formulas.
Tutorial
Even though there is more than one variable in a
formula, you solve
for a specific variable using the
exact
same steps that you do with an equation in one variable, as shown in
Tutorial
7: Linear Equations in One Variable.
It is really easy to get overwhelmed when there is more than one variable involved. Sometimes your head feels like it is spinning when you see all of those variables. Isn’t math suppose to be about numbers? Well, just remember that a variable represents a number, so if you need to move it to the other side of the equation you use inverse operations, just like you would do with a number.
In this problem, we need to solve for L. This means we need to get L on one side and EVERYTHING ELSE on the other side using inverse operations.
Let’s solve this formula for L:
*Inverse of mult. by 2 is div.
by 2
*Formula solved for L
In this problem, we need to solve for r. This means we need to get r on one side and EVERYTHING ELSE on the other side using inverse operations.
Let’s solve this formula for r:
*Inverse of mult. by 2pi is div. by 2pi
*Formula solved for r
In this problem, we need to solve for y. This means we need to get y on one side and EVERYTHING ELSE on the other side using inverse operations.
Let’s solve this formula for y:
*Inverse of mult. by 4 is div. by 4
*Formula solved for y
In this problem, we need to solve for h. This means we need to get h on one side and EVERYTHING ELSE on the other side using inverse operations.
Let’s solve this formula for h:
*Formula solved for h
Step 1: Understand the problem.
Step 2: Devise a plan (translate).
Step 3: Carry out the plan (solve).
Step 4: Look
back (check and
interpret).
Compound interest is a type of word problem that involves something that we all can relate to - MONEY, MONEY, MONEY!!!
Since we are looking for compound interest, we will need the compound interest formula:
The variables in this formula represent the following:
A = ending amount in the
account
P = principal (starting
amount)
r = annual rate of interest
t = time in years
n = number of times
compounded per year
In this problem,
A = ? = this is the variable we are looking for
P = 7000
r = 8% = .08
t = 9
n = 4 (There are
4 quarters
in a year)
Plugging the values into the formula we get:
*Add inside the ( )
*Raise 1.02 to the exponent of 36
*Multiply
FINAL ANSWER: The compound amount is $14279.21.
Since we are looking for speed, we can use the distance/rate formula:
d = rt
The variables in this formula represent the following:
d = distance
r = rate
t = time
d = rt
Plugging the values into the formula we get:
FINAL ANSWER: The average speed is 70 mph.
Since we are looking for the volume of a sphere, we can use this formula:
The variables in this formula represent the following:
V = volume of a sphere
r = radius
Plugging the values into the formula we get:
*Multiply
FINAL ANSWER: The volume of the beach ball is cubic inches.
Since we are needing to find the area of a rectangle, we can use this formula:
A = LW
The variables in this formula represent the following:
A = Area of a rectangle
L = length
W = width
In this problem,
A = ? = this is the variable
we are looking
for
L = 70
W = 50
A = LW
Plugging the values into the formula we get:
FINAL ANSWER: 7 bags of fertilizer.
To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problems 1a - 1b: Solve each equation for the specified variable.
Practice Problems 2a - 2c: Solve the following word problems.
Need Extra Help on these Topics?
http://www.purplemath.com/modules/solvelit.htm
This webpage helps you with solving formulas for a specified variable.
http://www.purplemath.com/modules/perimetr.htm
This webpage involves a
combination of problem
solving ideas from both Tutorial 8:
An Introduction to Problem Solving and Tutorial 9: Formulas and
Problem
Solving. It includes
problem
solving using formulas.
Go to Get Help Outside the Classroom found in Tutorial 1: How to Succeed in a Math Class for some more suggestions.
Last revised on July 3, 2011 by Kim Seward.
All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward. All rights reserved.