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SOLUTION

EXAMPLE 5. Write an inverse variation equation. Tell whether the table represents inverse variation. If so, write the inverse variation equation. SOLUTION. Find the products xy for all pairs (x, y):.

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SOLUTION

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  1. EXAMPLE 5 Write an inverse variation equation Tell whether the table represents inverse variation. If so, write the inverse variation equation. SOLUTION Find the products xy for all pairs (x, y): –5(2.4) = –12 –3(4) = –12 4(–3) = –12 8(–1.5) = –12 24(–0.5) = –12

  2. ANSWER The inverse variation equation isxy = –12, or y = . –12 x EXAMPLE 5 Write an inverse variation equation The products are equal to the same number,–12. So, y inversely withx.

  3. EXAMPLE 6 Solve a multi-step problem Theater A theater company plans to hire people to build a stage set. The work time t(in hours per person) varies inversely with the number pof people hired. The company estimates that 25 people working for 300 hours each can complete the job. Find the work time per person if the company hires 30 people.

  4. t = a p a 300 = 25 7500 The inverse variation equation ist = . p EXAMPLE 6 Solve a multi-step problem SOLUTION STEP 1 Write the inverse variation equation that relates pand t. Write inverse variation equation. Substitute25forpand300for t. 7500 =a Multiply each side by 25.

  5. = = 250. 30: t = Find t when p = 7500 ANSWER 30 If 30people are hired, the work time per person is 250 hours. 7500 p EXAMPLE 6 Solve a multi-step problem STEP 2

  6. ANSWER inverse variation; y = ANSWER –10 If 30people are hired, the work time per person is 180 hours. x for Examples 5 and 6 GUIDED PRACTICE 7. Tell whether the ordered pairs (–5, 2), (–4, 2.5), (8, –1.25), and (20, –0.5) represent inverse variation. If so, write the inverse variation equation. 8. WHAT IF? In Example 6, suppose the theater company estimates that 20 people working for 270 hours each can complete the job. Find the work time per person if the company hires 30 people.

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