A fruit drink is prepared by mixing water and fruit concentrate in a ratio of by volume. If Mia wants to make liters of the drink, how many liters of water will she need?
For mixture questions with a ratio and a total amount, first interpret the ratio as “parts” (for example, 5:1 means 5 parts water and 1 part concentrate, so 6 parts total). Divide the total amount by the total number of parts to find the size of one part, then multiply by the number of parts you care about. Always do a quick reasonableness check: the amount of an ingredient must be less than the total mixture and should match the proportion in the ratio.
Hints
Understand what 5:1 means
The ratio compares the volume of water to the volume of fruit concentrate. How many parts in total does this ratio represent?
Relate total parts to total volume
Once you know how many total parts there are, think about how you can use the 4.2 liters of drink to find the volume of just one part.
Use the number of water parts
After finding the volume of one part, multiply it by the number of parts that are water (from the ratio) to get the liters of water needed.
Desmos Guide
Compute the water volume with a fraction
In Desmos, type the expression (5/6)*4.2 and look at the numerical result; this value is the number of liters of water, since water is of the total drink.
Step-by-step Explanation
Interpret the ratio
The drink is mixed in a ratio of water to fruit concentrate.
- This means for every 5 equal parts of water, there is 1 equal part of concentrate.
- So there are total equal parts in the drink.
- Out of these 6 parts, 5 parts are water.
Find the volume of one part
The total volume of the drink is 4.2 liters, which corresponds to 6 equal parts.
To find the volume of 1 part, divide 4.2 liters by 6:
So each part (whether water or concentrate) is 0.7 liters.
Calculate the volume of water
Water makes up 5 of the 6 parts, and each part is 0.7 liters.
Multiply the number of water parts by the volume of one part:
So Mia needs 3.5 liters of water, which corresponds to answer choice B) 3.5.