Section 2.3 Formulas and Applications 79 5(59) = 5¢ 9 5 C≤ + 5(32) Multiply each side by the LCD, 5. 295 = 9C + 160 Simplify. 295 - 160 = 9C + 160 - 160 Subtract 160 from each side. 135 = 9C Simplify. 135 9C = 9 9 Divide each side by 9. 15 = C Simplify. So, the temperature of 59°F is equivalent to 15°C. Student Check 3 Use the appropriate formula to find the requested information. a. Use the compound interest formula to determine how much money is in an account if $20,000 is invested for 10 yr at 3.5% interest compounded annually. Round to the nearest cent. b. Use the compound interest formula to find how much money must be invested at 6% interest compounded annually to have $100,000 in an account after 5 yr. Round to the nearest cent. c. Use the Celsius-to-Fahrenheit conversion formula to find the value of F if C is 20°. d. Use the Celsius-to-Fahrenheit conversion formula to find the value of C if F = 104°. Solve Formulas for a Specified Variable At times, it is helpful to rewrite formulas so that a different variable is isolated. When asked to solve a formula for a specified variable, the goal is to isolate that variable on one side of the equation. The result will be another version of the given formula. We will use these skills in Chapter 3 when we rewrite linear equations in two variables in different forms. Example 4 parts (d) and (e) each illustrate this skill. Procedure: Solving a Formula for a Specific Variable Step 1: Clear fractions from the equation, if necessary. Step 2: Use the addition property of equality to get all terms with the appropriate variable on one side of an equation and the other terms on the other side. Simplify. Step 3: Use the multiplication property of equality to get a coefficient of 1 on the appropriate variable. Step 4: Simplify. Objective 4 Examples Solve each formula for the specified variable. 4a. d = rt is the distance formula. Solve this formula for r. 4b. P = 2l + 2w is the perimeter formula for a rectangle. Solve this formula for w. 4c. A = 1 2 bh is the area formula for a triangle. Solve this formula for b. 4d. 2x + y = 4; Solve this formula for y. 4e. 3x - 4y = 12; Solve this formula for y. Objective 4 ▶ Solve formulas for specified variables.
hendricks_intermediate_algebra_1e_ch1_3
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