Question

My recipe for one serving of fruit smoothie includes1 1/2 apples, 1/3 of a banana,1/5 of a mango and 5 raspberries. I want to make the smallest possible number of servings without having part of any fruit left over. How many raspberries do I need?

Answer 1

150

Explanation:

One serving need:

`(3)/(2)` apples,
`(1)/(3)` banana,
`(1)/(5)` mango, 5 raspberries

without having any fruit left over means:

all the fruit needed are integer

so we should find how many serves will cause the fruit needed are integer.

`(3)/(2)=(3*3*5)/(2*3*5)=(45)/(30)`

`(1)/(3)=(1*2*5)/(3*2*5)=(10)/(30)`

`(1)/(5)=(1*3*2)/(5*3*2)=(6)/(30)`

⇒ 30 serving need fruit 45 apple, 10 banana, 6 mango, and the raspberries need:

`5*30=150`

I hope this helps you

:)