Question

In a fruit punch drink the 3 ingredients are apple juice orange juice and cranberry juice. If 1/4 of the drink is apple juice and 2/5 is orange juice then write the ratio of cranberry juice to apple juice to orange juice in its simplest form.

Answer 1

Answer:  The required ratio in simplest form is 7 : 5 : 8.

Step-by-step explanation:  Given that in a fruit punch drink, the 3 ingredients are apple juice orange juice and cranberry juice. $\frac{1}{4}$ of the drink is apple juice and $\frac{2}{5}$ is orange juice.

We are to find  the ratio of cranberry juice to apple juice to orange juice in its simplest form.

Let x, y and z be the fractions of the cranberry juice, apple juice and orange juice in the fruit punch drink.

Then, according to the given information, we have

$y=\dfrac{1}{4},~~z=\dfrac{2}{5}.$

Now,

$x+y+z=1\\\\\\\Rightarrow x+\dfrac{1}{4}+\dfrac{2}{5}=1\\\\\\\Rightarrow x=1-\dfrac{1}{4}-\dfrac{2}{5}\\\\\\\Rightarrow x=\dfrac{20-5-8}{20}\\\\\\\Rightarrow x=\dfrac{7}{20}.$

Therefore, the ratio of cranberry juice to apple juice to orange juice is given by

$x:y:z\\\\\\=\dfrac{7}{20}:\dfrac{1}{4}:\dfrac{2}{5}\\\\\\=\dfrac{7}{20}:\dfrac{5}{20}:\dfrac{8}{20}\\\\=7:5:8.$

Thus, the required ratio in simplest form is 7 : 5 : 8.