Question 25·Easy·Ratios, Rates, Proportional Relationships, and Units
A fruit-punch recipe combines orange juice and pineapple juice in a constant ratio of cups of orange juice to cups of pineapple juice. If a cafeteria manager plans to use cups of orange juice, how many cups of pineapple juice are needed to keep the same ratio?
For ratio questions, translate the wording into a clear ratio (here, for orange to pineapple), then compare the original amount of one ingredient to the new amount to find the scale factor (18 is 6 times 3). Apply this same scale factor to the other part of the ratio (multiply 2 by 6) to find the missing quantity. As an alternative, you can set up a proportion like and solve by cross-multiplying, but always check that your final pair of numbers reduces to the original ratio.
Hints
Match the structure of the ratio
The recipe says the ratio of orange juice to pineapple juice is . Think of this as 3 cups of orange for every 2 cups of pineapple.
Compare original orange juice to the new amount
Originally, the ratio uses 3 cups of orange juice. The manager wants to use 18 cups. How many times larger is 18 than 3?
Apply the same change to pineapple juice
Whatever number you multiplied 3 by to get 18, multiply 2 by that same number to find the cups of pineapple juice needed.
Desmos Guide
Use a proportional expression in Desmos
In Desmos, type the expression 18 * 2 / 3 and look at the numeric result. This is the number of cups of pineapple juice needed to keep the ratio when using 18 cups of orange juice.
Step-by-step Explanation
Write the ratio clearly
The recipe uses a constant ratio of orange juice to pineapple juice of .
This means for every 3 cups of orange juice, there are 2 cups of pineapple juice.
Find the scale factor for orange juice
You are told the manager will use 18 cups of orange juice instead of 3.
Find how many times larger 18 is than 3:
So, the amount of orange juice is multiplied by 6 compared to the original recipe.
Scale the pineapple juice by the same factor
To keep the same ratio, multiply the pineapple part (2 cups) by the same factor of 6:
So the manager needs 12 cups of pineapple juice, which corresponds to answer choice C.