A smoothie shop mixes fruit concentrate and water in a ratio of by volume. If the shop makes liters of smoothie using this recipe, how many liters of fruit concentrate are used?
For ratio mixture questions, first add the ratio parts to find the total number of equal parts. Then divide the total quantity (like total liters) by this number to get the amount per part. Finally, multiply the per-part amount by the number of parts corresponding to the quantity the question asks for (here, the fruit concentrate). This avoids guesswork and is quick to compute, especially with simple decimals or fractions.
Hints
Combine the parts in the ratio
The ratio shows 2 parts of fruit concentrate and 7 parts of water. How many total parts is that?
Relate total parts to total liters
The liters of smoothie are divided into all the parts from the ratio. What operation should you use to find how many liters are in 1 part?
Focus on the fruit concentrate parts
Once you know the volume of 1 part, multiply it by the number of parts that are fruit concentrate (the first number in the ratio).
Desmos Guide
Compute the concentrate volume directly
In Desmos, type the expression 4.5 * (2/9) and press Enter. The output is the number of liters of fruit concentrate used in the smoothie.
Step-by-step Explanation
Understand the ratio
The recipe uses fruit concentrate and water in a ratio of by volume. This means that for every 2 parts of fruit concentrate, there are 7 parts of water. So the total number of equal parts in the mixture is
Find the volume of one part
The total smoothie volume is liters, and this is made up of equal parts.
To find the volume of one part, divide the total volume by the total number of parts:
Compute this value to see how many liters each part represents.
Calculate the fruit concentrate volume
From the previous step,
So each part of the mixture is liter. The fruit concentrate is of these parts, so
Therefore, the shop uses 1 liter of fruit concentrate.