# Beginning Algebra Tutorial 32

Beginning Algebra
Tutorial 32: Formulas

;   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:

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

*Formula solved for T

;   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:

*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

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:

The variables in this formula represent the following:

C = circumference of a circle

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)

Plugging the values into the formula we get:

First, find the circumference of a circle.

*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.

*Multiply

*Multiply using approx. value

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

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?

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:

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

Plugging the values into the formula we get:

*Square 4 and 5

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

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

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.

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 :

The variables in this formula represent the following:

= 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:

The variables in this formula represent the following:

= 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:

Plugging the values into the formula we get:

*Square 20 and 10

The area of the border is 80 square inches.