EXAMPLE 5 Solve a real-world problem SOLUTION SCIENCE As part of an environmental study, you need to...
8
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.
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Transcript of EXAMPLE 5 Solve a real-world problem SOLUTION SCIENCE As part of an environmental study, you need to...
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.
=2702
n150
=270 150 2 n
n=20,250
number of treesarea 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 ab
= 24 48
= 24 24 2
= 224
The geometric mean of 24 and 48 is 24 33.9.2
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.
=3903
n150
number of treesarea in acres
Write proportion.
Cross Products Property=390 150 3 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
9. 12 and 27
= 12 27
= 12 3 9
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
10. 18 and 54
= 318
= 18 18 3
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
11. 16 and 18
= 212
= 16 18
= 16 9 2
The geometric mean of 16 and 18 is 12 2
