Question

Bill made 5 gallons of fruit punch. If \[\dfrac{1}{4}\] of the punch was cranberry juice. Find the amount of cranberry juice used.

Answer 1

Hint: In the above stated question we know the overall amount of substance and now in this question we need to find out a particular amount of the substance for that we can multiply the required amount of substance with the amount of ratio stated in the question.

Complete step by step solution:
In the above question it is already stated that the overall amount of the substance that is fruit punch is five(5) gallons.
It is also mentioned that fruit punch is a mixture of different fruits and in the question it is asked that what is the amount of cranberry juice that is present in the fruit punch, for which in the question it is also mentioned that the amount of cranberry juice present in fruit punch is \[\dfrac{1}{4}\] of the overall fruit punch.
We can assume that fruit punch consists of 100 parts and out of which \[\dfrac{1}{4}\] of those 100 parts consist of cranberry juice, which we can also state as \[\dfrac{100}{4}=25\], with this we can say that out of 100 parts 25 parts is of cranberry juice.
We will be using the same concept in finding the amount of cranberry juice in 5 gallons of fruit punch.
To find the amount of cranberry juice in 5 gallons of fruit punch we will find out \[\Rightarrow \dfrac{5}{4}=1\dfrac{1}{4}=1.25\]\[\dfrac{1}{4}\] part of 5 gallons.
\[ \dfrac{5}{4}=1\dfrac{1}{4}=1.25\]
From the above statement we can say that \[\dfrac{1}{4}\] part of 5 is equal to 1.25, from which we can conclude that the amount of cranberry juice that is present in the fruit punch is equal to 1.25 gallons out of 5 gallons of fruit punch.

Note:
To solve this kind of problem we will always try to find the amount or part of the substance that we need to find which is stated in the question. Also try to change the fraction to decimal parts so as to easily calculate and find the answer.