70 Chapter 1 Linear Equations and Inequalities in One Variable Answer 2. 49° and 131° Solution: Let x represent the measure of one angle. Let represent the measure of the other angle. Recall that two angles are complementary if the sum of their measures is 90°. Therefore, a verbal model is Verbal model Mathematical equation Solve for x. 1One angle2 1the complement of the angle2 90° x 14x 102 90 5x 10 90 5x 100 4x 10 41202 x 20, 10 70 If then . The two angles are 20 and 70. Skill Practice 2. Two angles are supplementary, and the measure of one is 16° less than 3 times the other. Find their measures. 2. Literal Equations Literal equations are equations that contain several variables.A formula is a literal equation with a specific application. For example, the perimeter of a rectangle can be found by the formula P 2l 2w . In this equation, P is expressed in terms of l and w. However, in science and other branches of applied mathematics, formulas may be more useful in alternative forms. For example, the formula can be manipulated to solve for either l or w: Solve for l Solve for w P 2l 2w P 2l 2w P 2w 2l P 2l 2w Subtract 2w. Subtract 2l. P 2l w Divide by 2. Divide by 2. To solve a literal equation for a specified variable, use the addition, subtraction, multiplication, and division properties of equality. Applying a Literal Equation Example 3 Buckingham Fountain is one of Chicago’s most familiar landmarks.With 133 jets spraying a total of 14,000 gal of water per minute, Buckingham Fountain is one of the world’s largest fountains. The circumference of the fountain is approximately 880 ft. a. The circumference of a circle is given by C 2pr. Solve the equation for r. b. Use the equation from part (a) to find the radius and diameter of the fountain. Use 3.14 for p and round to the nearest foot. w P 2l 2 l P 2w 2 2 P 2w 2 l P 2l 2w x 20 4x 10
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