EXAMPLE 5 Solve a real-world problem SOLUTION SCIENCE As part of an environmental study, you need to estimate the number of trees in a 150 acre area. You.

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EXAMPLE 5 Solve a real-world problem SOLUTION 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. Write and solve a proportion involving two ratios that compare the number of trees with the area of the land.

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

EXAMPLE 6 Find a geometric mean Simplify. Definition of geometric mean Substitute 24 for a and 48 for b. Factor. Find the geometric mean of 24 and 48. SOLUTION = x abab = = = 224 The geometric mean of 24 and 48 is

GUIDED PRACTICE for Examples 5 and 6 SOLUTION Write and solve a proportion involving two ratios that compare the number of trees with the area of the land. = n 150 number of trees area in acres Write proportion. Cross Products Property = n n = 19,500 Simplify. 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. 8.

GUIDED PRACTICE for Examples 5 and 6 ANSWER There are about 19,500 in the 150 acre area

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

GUIDED PRACTICE for Examples 5 and 6 Find the geometric mean of the two numbers. Simplify. Definition of geometric mean Substitute 18 for a and 54 for b. Factor. SOLUTION = 18 54= x ab and 54 =318 = The geometric mean of 18 and 54 is 18 3

GUIDED PRACTICE for Examples 5 and 6 Find the geometric mean of the two numbers. Simplify. Definition of geometric mean Substitute 16 for a and 18 for b. Factor. SOLUTION = x ab and 18 =212 = = The geometric mean of 16 and 18 is 12 2