Proportion Method - Algebra
PROPORTION METHOD
The proportion method is used in both of these expressions. A proportion is an equation that says that two ratios are equivalent. The use of cross multiplying is in use in both expressions as well. I believe the first expression (#56) uses the extreme-means property; the product of the means is equal to the product of the extremes.
#56. 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 will use b for bears and write the expression as follows: B x 100
50 2
I will cross multiply: 50 * 100 = 5,000 and B * 2 = 2B
5,000 = 2,500 2B
What is the estimate of the size of the bear population? The answer is 2,500. In this expression since the population of bears is unknown, I use B as the top of the ratio. There was 50 bears that were captured, tagged, and released, so this makes the bottom of the ratio. Now since there were 100 bears found and only 2 were tagged, 100 will be the top of the other ratio and 2 will be on the bottom. Then I cross multiply and divide the bottom of the ratio into the top to come up with the answer.
#10. y - 1 = - ¾ x + 3
4(y - 1) = -3(x + 3) Cross multiply.
4y – 4 = - 3x - 9 Multiply parentheses.
4y = - 3x - 5 Add 4 to both sides. y = - ¾ x - 5/4 Divide 4 from 4y by both sides.
Answer: y = - ¾ x – 5/4
The proportion method is used in both of these expressions. A proportion is an equation that says that two ratios are equivalent. The use of cross multiplying is in use in both expressions as well. I believe the first expression (#56) uses the extreme-means property; the product of the means is equal to the product of the extremes.
#56. 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 will use b for bears and write the expression as follows: B x 100
50 2
I will cross multiply: 50 * 100 = 5,000 and B * 2 = 2B
5,000 = 2,500 2B
What is the estimate of the size of the bear population? The answer is 2,500. In this expression since the population of bears is unknown, I use B as the top of the ratio. There was 50 bears that were captured, tagged, and released, so this makes the bottom of the ratio. Now since there were 100 bears found and only 2 were tagged, 100 will be the top of the other ratio and 2 will be on the bottom. Then I cross multiply and divide the bottom of the ratio into the top to come up with the answer.
#10. y - 1 = - ¾ x + 3
4(y - 1) = -3(x + 3) Cross multiply.
4y – 4 = - 3x - 9 Multiply parentheses.
4y = - 3x - 5 Add 4 to both sides. y = - ¾ x - 5/4 Divide 4 from 4y by both sides.
Answer: y = - ¾ x – 5/4