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Beginning Algebra
Answer/Discussion to Practice Problems
Tutorial 32: Formulas



 

checkAnswer/Discussion to 1a
problem 1a;   for T

 
Do you recognize this formula?
This happens to be the formula for simple interest, where I = simple interest, P = principal, R = annual percentage rate, and T = time in years.

In this problem we need to solve for T.  This means we need to get T on one side and EVERYTHING ELSE on the other side using inverse operations.

Let’s solve this formula for T:


 
ad1a

*Inverse of mult. by PR is div. by PR
 

*Formula solved for T
 


 

 


 

checkAnswer/Discussion to 1b
problem 1b;   for y

 
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:


 
ad1b

*Inverse of add 3x is sub. 3x
 

*Inverse of mult. by -7 is div. by -7

*Formula solved for y
 
 

*Divide num. by -7
*Another way to write it
 


 

 


 

checkAnswer/Discussion to 2a
Sally is training for the Olympics.  She likes to run around  a circular track that has a diameter of 60 yards, 20 times during a workout.  How many yards does she run during her workout?

 
Step 1: Identify the type(s) of  figure(s) in the problem. 
AND
Step 2:  Identify what formula(s) you need. 

 
Make sure that you read the question carefully several times. 

Since we are needing to find the circumference of a circle,  we can use this formula:

ad2a1

The variables in this formula represent the following:

C = circumference of a circle
r = radius


 
Step 3:  Put the problem together.

 
In this problem, 
C = ? = this is the variable we are looking for
r = 30  (radius is half of the diameter, so r = 60/2 = 30)

ad2a1

Plugging the values into the formula we get:

ad2a2


 
First, find the circumference of a circle.

 
ad2a3

*Multiply
 

*Replace pi with 3.14 for an approximate value

 


 
For every workout, she runs around the track 20 times.  So, we need to multiply the circumference by 20 to find the number of yards that she runs during her workout.

 
ad2a5
*Multiply

*Multiply using approx. value


 
FINAL ANSWER: 

The number of yards that she runs in a workout is 1200example 2b or approximately 3768.


 

 


 

checkAnswer/Discussion to 2b
A ramp 5 feet long is leaning against a raised platform which is 4 feet above the ground.  What is the distance from the ramp’s contact point with the ground and the base of the platform?

ad2b1


 
 
Step 1: Identify the type(s) of  figure(s) in the problem. 
AND
Step 2:  Identify what formula(s) you need. 

 
Make sure that you read the question carefully several times. 

Since we are looking for the side of a right triangle,  we can use the Pythagorean formula:

example 7a
example 7d

The variables in this formula represent the following:

a and b = legs of the right triangle
c = hypotenuse of the right triangle


 
Step 3:  Put the problem together.

 
In this problem, 
a = ? = this is the variable we are looking for
b = 4
c = 5 

example 7a

Plugging the values into the formula we get:

ad2b3


 
ad2b2

*Square 4 and 5

*Subtract 16 from both sides
*What squared gives you 9?


 
FINAL ANSWER: 

The distance from the ramp’s contact point with the ground and the base of the platform is 3.


 

 


 

checkAnswer/Discussion to 2c
In the figure, ABCD is a square, with each side of length 8 inches.  The width of the border (shaded portion) between the outer square EFGH and ABCD is 2 inches.  Find the area of the border.

ad2c1


 
Step 1: Identify the type(s) of  figure(s) in the problem. 
AND
Step 2:  Identify what formula(s) you need. 

 
Make sure that you read the question carefully several times. 

Since part of the problem involves the area of the big square, we can use the formula :

ad2c4

The variables in this formula represent the following:

example 9g = area of the big square
s1= side of the big square
 

Since part of the problem involves the area of the inner square, we can use also use the formula:

ad2c5

The variables in this formula represent the following:

example 9h = area of the inner square
s2= side of the inner square



 
Step 3:  Put the problem together.

 
In this problem, 
A = ? = this is the variable we are looking for
s1 = 8 + 2 + 2 = 12
s2 = 8

If we take the area of the bigger square and subtract out the area of the smaller square we will have the area of the border:

ad2c2

Plugging the values into the formula we get:

ad2c6


 
ad2c3

*Square 20 and 10

 
FINAL ANSWER: 

The area of the border is 80 square inches.


 

 

Buffalo Top

 


Last revised on August 3, 2011 by Kim Seward.
All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward. All rights reserved.