Solving Proportions
MAT 222 Intermediate Algebra
Nalla Lorto
March 24, 2013

Solving Proportions

Problem 1

Bear population. To 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?

I think using a simple ratio equation would work here, let b = bear population
=
cross multiply
2b = 50*100

2b=5000 divide 2 by 5000

5000 =b
2

b=2500 answer

Problem 2
For the second problem in this assignment I am asked to solve this equation for y. The first thing I notice is that it is a single fraction (ratio) on both sides of the equal sign so basically it is a proportion which can be solved by cross multiplying the extremes and means.

y-1 = -3 this problem is a proportion x+3 4

y-1 (x+3 = -3 (x+3) multiply both sides by x+3 – using the extreme means x+3 4 property

y-1= -3x+3 add 1 to 3. A number that appears to be a solution but causes 4 0 in a denominator is called an extraneous solutions

y=-3x+4 4 answer The form of equation I ended up with in problem 10 would be a linear equation. I noticed that the coefficient of x is different than the original problem is that x+3 and in my problem it is -3x/4. I could solve the problem by cross multiply at the beginning of the problem.

Reference
Dugopolski, M. (2011). Elementary & Intermediate Algebra. New York : McGraw-Hill.