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.

Question

10-11-2020
Mathematics

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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.

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boffeemadrid boffeemadrid · Answer 1 · 2020-11-14T13:03:52+01:00

Answer:

[tex]\dfrac{8}{3}\ \text{cups of orange juice}[/tex] or [tex]2\dfrac{2}{3}\ \text{cups of orange juice}[/tex] is used

Step-by-step explanation:

Daniel uses the proportions of [tex]\dfrac{2}{3}[/tex] cups of orange juice and [tex]\dfrac{1}{4}[/tex] 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.

[tex]\dfrac{2}{3}\ \text{cups of orange juice}=\dfrac{1}{4}\ \text{cups of carrot juice}\\\Rightarrow 4\times \dfrac{2}{3}\ \text{cups of orange juice}=4\times \dfrac{1}{4}\ \text{cups of carrot juice}\\\Rightarrow \dfrac{8}{3}\ \text{cups of orange juice}=1\ \text{cup of carrot juice}[/tex]

So for one cup of carrot juice [tex]\dfrac{8}{3}\ \text{cups of orange juice}[/tex] or [tex]2\dfrac{2}{3}\ \text{cups of orange juice}[/tex] is used.