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DETAILED SOLUTIONS AND CONCEPTS - FORMULAS AND WORD PROBLEMS
Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada
Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you!
PLEASE NOTE THAT YOU CANNOT USE A CALCULATOR ON THE ACCUPLACER ELEMENTARY ALGEBRA TEST! YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS
WITHOUT A CALCULATOR!
Formula rearrangement refers to isolating a letter term other than the one already isolated in the formula. Solving formulas in the manner often shortens our work when doing repeated formula evaluations. After we solve the formula for the desired variable, we rewrite the formula with the variable on the left side for convenience and for use in electronic spreadsheets.
Problem 1:
Solve the "mark up" formula M = S - C for S.
To solve the equation above, we will use the Addition Axiom to isolate the variable S by
"moving" all terms associated with S by addition away from the variable.
The variable associated with S by addition is C. Therefore, we must add C to both sides of the equation.

M+C=S-C+C and M + C = S
Finally, we rewrite the formula with S on the left

S=M+C
Problem 2:
Solve the interest formula I = PRT for R. It stands for Interest = Principal
Time.

Rate

To solve the equation above, we will use the Multiplication Axiom to isolate the variable R by "moving" all terms associated with R by addition away from the variable.
The variables associated by multiplication with R are P

T or PT. Therefore, we will

multiply both sides of the equation by its reciprocal **, which is

.

** Interchanging the numerator and denominator of a fraction results in a fraction that is called the reciprocal of the original fraction. When a number is multiplied by its reciprocal, the product equals 1.

Carrying out the multiplications, we get

which should be presented as

.

Problem 3:

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