# mat222 wk1 solving proportions

Solving Proportions

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MAT 222 Week 1 Assignment

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Solving Proportions

Proportions exist in many real-world applications, and in this problem

estimating the size of the bear population on the Keweenaw Peninsula. By comparing

data from two experiments, conservationists are able to predict patterns of animal

increase or decrease. In this situation, 50 bears were captured and tagged and released to

estimate the size of the bear population. A year later, after capturing a random sample of

100 bears only 2 of the bears captured were tagged bears. These proportions will be used

to determine the bear population on the peninsula. This new bear scenario can be solved

by applying the concept of proportions which allows the assumption of the ratio of

originally tagged bears to the whole population is equal to the ratio of recaptured tagged

bears to the size of the sample. To determine the estimated solution, the bears will be the

extraneous variables that will be defined for solving the proportions used.

Problem #56, page 437

50The ratio of originally tagged bears to the whole population X

_2_The ratio of recaptured tagged bears to the sample size 100

50 = _2_ This is the proportion set up and ready to solve. X 100

(50)(100), (X)(2)The next step is to cross multiply.

5000 = 2XDivide both sides by 2

2 2

2500 = XThe bear population on the Keweenaw Peninsula is estimated to be

around 2500.

The extreme means for this sample were 50 and 100, X and 2.

For the second problem in this assignment, the equation must be solved for Y.

Continuing the discussion of proportions, a single fraction (ratio) exists on both sides

of the equal sign so basically it is a proportion, which can be solved by cross

multiplying the...

References: Elementary and Intermediate Algebra, 4th Ed., Dugopolski

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