Solving a proportion means that you are missing an import number in your equation or fraction and you need to solve for that missing value. It is a comparison of ratios and an equation that states that two ratios are equal. In each proportion the first and last terms are called the extremes and the second and third terms are called the means. If the fractions both reduce to the same value, the proportion is true. In a true proportion the product of the means equals the product of the extremes. Proportions can also be solved by multiplying each side of the proportion by the common denominator for both fractions.
When solving equations involving rational expressions, we must check every solution to see whether it causes 0 to appear in a denominator. If a number causes the denominator to be 0, then it cannot be a solution to the equation. A number that appears to be a solution but causes 0 in a denominator is called an extraneous solution. Since a solution to an equation is sometimes called a root to the equation, an extraneous solution is also called an extraneous root. (Dugopolski, M. 2012)
For this week’s assignment we were asked to work through two proportions. For the first proportion, number 56 on page 437 of Elementary and Intermediate Algebra by Dugopolski, estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist’s estimate of the size of the bear population? The second proportion is to complete problem 10 on page 444.
Beginning to solve the first equation, we need to estimate the size of the bear population located on the Keweenaw Peninsula conservation. We are to make a proportion with the number of tagged bears in the sample and in the number of bears that are estimated in population. We are to assume that the ratio of originally tagged bears to the whole population...