Question

There are 32 munchkins in the box. You want to distribute the munchkins to Amir and Isaac so that the ratio of Amir's munchkins to Isaacs is 5:8.

How many munchkins will each person get? Show/explain your work

Answer 1

Amir will get 160/13 or 12
`(4)/(13)` and Isaac will get 20
`(9)/(13)`

Explanation:

Lets say that the ratio is
`5x:8x`. Then, let's put this into an equation:

`5x+8x=32`

Then, if we solve, we get:

`13x=32, x=(32)/(13) \text{ or } 2(6)/(13)\\`

Then, we know that Amir's share is
`5x`, so
`(32)/(13)\cdot5=160/13 \text{ or } 12 (4)/(13)`.

Then, Isaacs share is
`8x`, so
`8\cdot(32)/(13)=20(9)/(13)`

Hope it helps!!

Answer 2

Amir = 12 and Isaac = 20

Explanation:

Given

`Amir : Isaac = 5 : 8`

`Munchkins = 32`

Required

Amount of munchkins given to each person

For Amir, the amount is calculated as:

`Amir's = (Amir)/(Amir + Isaac) * Munchkins`

`Amir's = (5)/(5+8) * 32`

`Amir's = (5)/(13) * 32`

`Amir's = (5 * 32)/(13)`

`Amir's = (160)/(13)`

`Amir's \approx 12`

For Isaac, the amount is calculated as:

`Isaac's = (Isaac)/(Amir + Isaac) * Munchkins`

`Isaac's = (8)/(5 + 8) * 32`

`Isaac's = (8)/(13) * 32`

`Isaac's = (8 * 32)/(13)`

`Isaac's = (256)/(13)`

`Isaac's \approx 20`