Equivalent Ratios

Part of the Decimals, Percents & Ratios section of Coddy's Pre-Algebra journey. Lesson 39 of 56.

Equivalent ratios describe the same mix with different numbers. A paint recipe uses 2 cups of blue for every 5 cups of white. You want a bigger batch with 15 cups of white. How much blue? Write the two ratios, blue over white, as equal fractions: 2/5 = n/15, where n is the blue you need.

Find the scale factor: the white went from 5 cups to 15, and 5 times 3 is 15, so the batch is 3 times bigger. The blue must grow by the same factor: 2 times 3 is 6, so n = 6. Both parts are multiplied by the same number, which keeps the colour the same. Tripling only the white would give a much paler paint.

On the board the two ratios are written for you, with the missing number as a letter. There are no moves to press: you work out the number yourself and type your claim, like n = 6.

Challenge

A drink mixes 3 cups of juice for every 4 cups of water. A bigger batch uses 20 cups of water. The board shows the two ratios, juice over water. Find the juice n for the big batch and type your claim, like n = ..., then press Check.

Try it yourself

3/4 = n/20

Solve for n