# Proportions

**Topics:**Elementary arithmetic, Equals sign, Problem solving

**Pages:**3 (454 words)

**Published:**June 5, 2014

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.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...

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