Easy Mathematics Step-by-Step (2012)

Chapter 12. Formulas

In this chapter, you evaluate formulas.

Definition of Formula

A formula is a rule that shows the mathematical relationship that connects two or more variables. Formulas are used extensively in mathematics, the natural and social sciences, engineering, and numerous other areas in the real world. You use your skills in evaluating algebraic expressions to evaluate formulas.

Evaluating Formulas

The symbols and/or letters in a formula are variables (except for special constants like π and e). If you are given numerical values for the variables, you evaluate the formula by substituting the given numerical value for each variable and then performing the indicated operations, being sure to follow the order of operations as you proceed.

If units are involved, carry the units term along in the computation, when it makes sense to do so. When you add or subtract units, the sum or difference has the same units. When you square a unit (i.e., unit × unit), you get unit². When you cube a unit (i.e., unit × unit × unit), you get unit³.

Problem Evaluate the formula to find the value of the indicated variable.

a. Find C when using the formula .

b. Find P when m using the formula .

c. Find positive value c when and using the formula .

d. Find A when ft and ft using the formula .

e. Find I when , per year, and yr using the formula .

f. Find A when yd using the formula . Use .

g. Find V when cm and cm using the formula . Use .

h. Find d when mi per hour and hr using the formula .

Solution

a. Find C when using the formula

Step 1. Substitute 212 for F in the formula

Step 2. Evaluate.

b. Find P when m using the formula .

Step 1. Substitute 8 m for s in the formula .

Step 2. Evaluate.

c. Find positive value c when and using the formula .

Step 1. Substitute 8 for a and 15 for b in the formula

Step 2. Evaluate.

To obtain c, you must find the positive square root of 289. From the list of square roots in Chapter 10, you have .

Thus, .

d. Find A when ft and ft using the formula .

Step 1. Substitute 10 ft for l and 4 ft for w in the formula .

Step 2. Evaluate.

e. Find I when P = $3000, r = 4% per year, and yr using the formula I = Prt.

Step 1. Substitute $3000 for P, for r, and 5 yr for t in the formula

Put quantities that follow the word per in the denominator of a fraction.

Step 2. Evaluate.

Notice that the “yr” units divide out, leaving “$” as the units for the answer.

f. Find A when yd using the formula Use .

Step 1. Substitute 6 yd for r and 3.14 for π in the formula .

Step 2. Evaluate.

g. Find V when cm and cm using the formula . Use .

Step 1. Substitute 2.5 cm for r, 11.5 cm for h, and 3.14 for π in the formula

Step 2. Evaluate.

h. Find d when mi per hour and hr using the formula .

Step 1. Substitute for r and 5 hr for t in the formula .

Step 2. Evaluate.

Notice that the “hr” units divide out, leaving “mi” as the units for the answer.

Exercise 12

Evaluate the formula to find the value of the indicated variable.

1. Find C when using the formula .

2. Find P when m using the formula .

3. Find positive value c when and b = 24 using the formula .

4. Find A when ft and ft using the formula A = lw.

5. Find I when , r = 3% per year, and yr using the formula I = Prt.

6. Find A when yd using the formula Use .

7. Find V when ft and ft using the formula . Use .

8. Find A when and using the formula .

9. Find V when cm and cm using the formula . Use .

10. Find F when using the formula .