Question

Daniel uses \large \frac{2}{3}cup of orange juice for every \large \frac{1}{4}cup of carrot juice to make his drink. Enter the number of cups of orange juice Daniel uses for 1 cup of carrot juice. Enter answer as an improper fraction (ex. 7/3) or mixed number (ex. 2 1/3). Daniel uses cups of orange juice for 1 cup of carrot juice.

Answer 1

`(8)/(3)\ \text{cups of orange juice}` or
`2(2)/(3)\ \text{cups of orange juice}` is used

Explanation:

Daniel uses the proportions of
`(2)/(3)` cups of orange juice and
`(1)/(4)` cups of carrot juice to make a mixed juice.

Now, in the question 1 cup of carrot juice is used. So 4 times of the proportion of the carrot juice is used. Accordingly 4 times of the cups of orange juice will be used.

`(2)/(3)\ \text{cups of orange juice}=(1)/(4)\ \text{cups of carrot juice}\\\Rightarrow 4* (2)/(3)\ \text{cups of orange juice}=4* (1)/(4)\ \text{cups of carrot juice}\\\Rightarrow (8)/(3)\ \text{cups of orange juice}=1\ \text{cup of carrot juice}`

So for one cup of carrot juice
`(8)/(3)\ \text{cups of orange juice}` or
`2(2)/(3)\ \text{cups of orange juice}` is used.