6th grade proportions

[Bryce255]

Adam and Bill are co-owners of a bookstore. They share the profits of the store in a ratio of 4 to 5, respectively. The profits for several items are shown below. Determine the amount of profit each person receives on the sale of each item. comic books 30cents used paperback book 75 cents new paperback book $1.25 puzzle $2.39 best-seller $3.75. What is the formula that you use to solve this problem?

 

[tkhunny]

Your challenge is to divide the profits in the proper ratio.

If the profit were 9¢, it would be easy. 4¢ and 5¢
If the profit were 18¢, it would be easy. 8¢ and 10¢
If the profit were 36¢, it would be easy. 16¢ and 20¢

In each case, the solution is the sum of 4¢ and 5¢ each multiplied by the same number.

If the profit were 9¢, it would be easy. 1*4¢ and 1*5¢
If the profit were 18¢, it would be easy. 2*8¢ and 2*10¢
If the profit were 36¢, it would be easy. 4*16¢ and 4*20¢

You just need that number!


A good way to find the number, is a proportion. Generally, compare one profit to the total, like this: \(\displaystyle \dfrac{4}{9} = \dfrac{A}{0.30}\) in the case of the 30¢profit.

Where does that leave us?

 

[HallsofIvy]

4+ 5= 9. So given any amount "A", divide by 9 to find one "part". Adam then takes four "parts" or (4/9)A and Bill takes 5 "parts" or (5/9)A.