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EXAMPLE 5

SCIENCE. As part of an environmental study, you need to estimate the number of trees in a 150 acre area. You count 270 trees in a 2 acre area and you notice that the trees seem to be evenly distributed. Estimate the total number of trees. EXAMPLE 5. Solve a real-world problem. SOLUTION.

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EXAMPLE 5

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  1. SCIENCE As part of an environmental study, you need to estimate the number of trees in a 150 acre area. You count 270 trees in a 2 acre area and you notice that the trees seem to be evenly distributed. Estimate the total number of trees. EXAMPLE 5 Solve a real-world problem SOLUTION Write and solve a proportion involving two ratios that compare the number of trees with the area of the land.

  2. n number of trees = 150 area in acres 270 150 = 20,250 270 n = 2 2 n EXAMPLE 5 Solve a real-world problem Write proportion. Cross Products Property Simplify. There are about 20,250 trees in the 150 acre area.

  3. = ab x 2448 = 24 24 2 = = 24 2 The geometric mean of 24 and 48 is 2433.9. 2 EXAMPLE 6 Find a geometric mean Find the geometric mean of 24 and 48. SOLUTION Definition of geometric mean Substitute 24 for a and 48 for b. Factor. Simplify.

  4. n number of trees 8. WHAT IF ?In Example 5, suppose you count 390 trees in a 3 acre area of the 150 acre area. Make a new estimate of the total number of trees. 150 area in acres 390 150 = 390 3 = 3 n 19,500 n = for Examples 5 and 6 GUIDED PRACTICE SOLUTION Write and solve a proportion involving two ratios that compare the number of trees with the area of the land. Write proportion. Cross Products Property Simplify.

  5. ANSWER There are about19,500in the150acre area for Examples 5 and 6 GUIDED PRACTICE

  6. ab = x 12 27 = 12 3 9 = = 18 for Examples 5 and 6 GUIDED PRACTICE Find the geometric mean of the two numbers. 9.12 and 27 SOLUTION Definition of geometric mean Substitute 12 for a and 27 for b. Factor. Simplify. The geometric mean of 12 and 27 is 18

  7. ab = x 18 54 = 18 18 3 = = 18 3 The geometric mean of 18 and 54 is 18 3 for Examples 5 and 6 GUIDED PRACTICE Find the geometric mean of the two numbers. 10.18 and 54 SOLUTION Definition of geometric mean Substitute 18 for a and 54 for b. Factor. Simplify.

  8. ab = x 16 18 = 16 9 2 = = 12 2 The geometric mean of 16 and 18 is 12 2 for Examples 5 and 6 GUIDED PRACTICE Find the geometric mean of the two numbers. 11.16 and 18 SOLUTION Definition of geometric mean Substitute 16 for a and 18 for b. Factor. Simplify.

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