Question 23·Medium·Ratios, Rates, Proportional Relationships, and Units
A smoothie recipe uses strawberries and yogurt in a ratio of by volume. If a café wants to prepare cups of the smoothie using the same ratio, how many cups of strawberries are needed?
For ratio questions where a total amount is given, first add the parts in the ratio to find the total number of equal parts. Divide the total quantity by this number to get the size of one part, then multiply by the number of parts for the quantity you care about. This "parts of a whole" method is quick, avoids setting up full equations, and works reliably under time pressure.
Hints
Add the parts in the ratio
In the ratio , think of "parts." How many total parts are there when you add the strawberry parts and yogurt parts together?
Relate total parts to total cups
Those total parts together make 40 cups. How can you use division to find how many cups correspond to 1 part?
Use the number of strawberry parts
Once you know how many cups are in 1 part, multiply by the number of strawberry parts in the ratio (which is 3).
Desmos Guide
Compute the strawberry amount directly
In Desmos, type 3/5*40 and press Enter. The value shown is the number of cups of strawberries needed (because strawberries are 3 out of 5 total parts of the smoothie).
Step-by-step Explanation
Interpret the ratio
The ratio (strawberries : yogurt) means that in every "batch" of the smoothie there are:
- 3 equal parts of strawberries
- 2 equal parts of yogurt
So there are equal parts in the total mixture.
Find the size of one part
Those 5 equal parts together make the 40 cups of smoothie.
So each part has volume
Find the amount of strawberries
Strawberries make up 3 of the 5 parts, and each part is 8 cups.
So the amount of strawberries is
Therefore, the café needs 24 cups of strawberries.