Solving Porpotions

Solving Proportions

Proportion is two equal ratios by estimating the amount and size of the bear’s population. In order to determine the estimated size of the animals, conservationists must conduct at least two experiments to see if the populations have decrease or increase. In this latitude 50 bears were captured and release to figure out the estimating size of the bear population. A year later some samples were collected by some random 100 bears and only 2 of the tagged bears.

The new bear scenario can be applied by using the same proportion in problem # 56 on page 437 (Dugolpolski, 2012), so in order to determine the estimated solution, using the variables will help to find the rules for solving the proportions. Let’s make "x" the number of the total bear population.

The ratio of originally tagged bears to the whole population would be 50/x the ratio of recaptured tagged bears to the sample size would be 2/100,

50 = 2 This is the proportion set up and ready to solve.

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

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

5000 = 2x Divide both sides by 2

2 2

2500 = x The population of the bears on the Keweenaw Peninsula is estimated to be

2500.

The second part of the assignment, the following equation must be solved for y. Since there are single fractions ratios on both sides of the equation, the extreme means property will be used again in this proportion.

(y – 1)/(x+3)=-3/4 Written as an equation; solving for y.

4(y – 1) = -3x(x + 3) Cross multiplying was done.

4y – 1 + 4 = -3x +3 +3 Distribute 4 on left side and 3 on the right side.

y = -3x -3 + 1 Add 1 to both sides.

4y = 2x -5 Last step, 4 is divided on both sides.

4 4

y = -3

4 Linear equation in the form of y = mx + b and with a slope of -3/4....