A smoothie shop uses 12 ounces of fruit puree to prepare 3 medium smoothies. At this same rate, how many ounces of fruit puree are needed to prepare 10 medium smoothies?
For ratio and proportion questions like this, quickly find the unit rate (amount per 1 item) by dividing, then multiply by the desired number of items. Alternatively, set up a clear proportion with matching units in numerator and numerator (and denominator and denominator), simplify step by step, and double-check that your scaling matches the target quantity (here, 10 smoothies).
Hints
Use unit rate
First figure out how many ounces of puree are needed for 1 smoothie by dividing the total ounces by the number of smoothies.
Then scale to 10 smoothies
Once you know the number of ounces for 1 smoothie, multiply that number by 10 to get the amount for 10 smoothies.
Alternative: set up a proportion
You can also write a proportion like , where is the number of ounces needed for 10 smoothies, and then solve for . Be careful with your multiplication and division.
Desmos Guide
Compute the needed ounces directly
In a Desmos expression line, type (12/3)*10 and press Enter. The value that Desmos outputs is the total number of ounces of fruit puree needed for 10 smoothies at the given rate.
Step-by-step Explanation
Find the amount of puree per smoothie
You are told that 12 ounces of fruit puree make 3 smoothies.
To find how many ounces are used for 1 smoothie, divide the ounces by the number of smoothies:
So each medium smoothie uses 4 ounces of fruit puree.
Scale up to 10 smoothies
Now use the rate you found: 4 ounces per smoothie.
For 10 smoothies, multiply the per-smoothie amount by 10:
So 40 ounces of fruit puree are needed to prepare 10 medium smoothies.