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

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Answer/Discussion to 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:

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

*Formula solved for T

(return to problem 1a)

Answer/Discussion to 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:

*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

(return to problem 1b)

Answer/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:

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)

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

FINAL ANSWER:

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

(return to problem 2a)

Answer/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?

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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 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

Plugging the values into the formula we get:

*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.

(return to problem 2b)

Answer/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.

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