Sharing in a Ratio

Part of the Decimals, Percents & Ratios section of Coddy's Pre-Algebra journey. Lesson 40 of 56.

Mia and Leo share 24 marbles in the ratio 5 to 3. Think in parts: Mia gets 5 parts and Leo gets 3, so there are 5 + 3 = 8 equal parts in all. Each part is 24 divided by 8, which is 3 marbles. Mia's 5 parts make 15 marbles and Leo's 3 parts make 9.

A shorter way: Mia gets 5 of the 8 parts, so her share is 5/8 of all the marbles, and a fraction of a number is a product. Use a for her share: a = 24 × (5/8), and on the next line a = 15. The ratio 5 to 3 is part to part; the fraction of the whole uses the part to whole ratio, 5 to 8.

Check by adding the shares back: 15 + 9 is 24, the whole amount. The common slip is dividing by one of the ratio numbers instead of the total number of parts. 24 divided by 5 is not even a whole number of marbles, a sign that something went wrong.

Challenge

A coach shares 35 sweets between the girls and the boys of a club in the ratio 3 to 2, girls to boys. Find the girls' share g. Write g equal to the calculation, then work it out on the next line.