how many cups of oj and kiwi juice would you require?

Question

A drink recipe calls for $\frac{1}{4}$ cup of orange juice and $\frac{1}{6}$ cup of kiwi juice. If you have a total of $\frac{10}{3}$ cups of fruit, how many cups of oj and kiwi juice would you require?

Hi everyone! I know that you need 2 cups of OJ and $\frac{4}{3}$ cups of kiwi juice. However, I have no idea how to explain it.

What I did was found the total number of fruits i have which is $\frac{5}{12}$ then I divided $\frac{1}{4}$ by $\frac{5}{12}$ to get $\frac{3}{5}$ and I multiplied that by $\frac{10}{3}$. Honestly, I know how to solve this problem but I dont know what each step means. Can anyone explain?

Answer 1

Ratio of oj and kiwi $=\frac1{4} : \frac1{6} = 3:2$
So, that ratio will remain in $10/3$ cups juice also.
Let $3x$ be amount of oj, then

$3x+2x = 10/3\qquad$(total fruits)
So, $3x= 10/3 * \frac 1{5} * 3 = 2=$cups of oj

Answer 2

Clearly, since you got that far, the single-recipe quantity of $\frac 5{12}$ cups of juice gets that you have $\left .\frac{10}{3}\middle /\frac{5}{12}\right . = \frac{10\cdot 12}{3\cdot 5} =8$ recipe-quantities to work with.

So you need - as you say - $8\times \frac 14 = 2$ cups of orange juice and $8\times \frac 16 = \frac 43$ cups of kiwi.