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.
`(1)/(4)` of the drink is apple juice and
`(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=(1)/(4),~~z=(2)/(5).`

Now,

`x+y+z=1\\\\\\\Rightarrow x+(1)/(4)+(2)/(5)=1\\\\\\\Rightarrow x=1-(1)/(4)-(2)/(5)\\\\\\\Rightarrow x=(20-5-8)/(20)\\\\\\\Rightarrow x=(7)/(20).`

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

`x:y:z\\\\\\=(7)/(20):(1)/(4):(2)/(5)\\\\\\=(7)/(20):(5)/(20):(8)/(20)\\\\=7:5:8.`

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