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:

Amir will get 160/13 or 12 [tex]\frac{4}{13}[/tex] and Isaac will get 20 [tex]\frac{9}{13}[/tex]

Step-by-step explanation:

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

[tex]5x+8x=32[/tex]

Then, if we solve, we get:

[tex]13x=32, x=\frac{32}{13} \text{ or } 2\frac{6}{13}\\[/tex]

Then, we know that Amir's share is [tex]5x[/tex], so [tex]\frac{32}{13}\cdot5=160/13 \text{ or } 12 \frac{4}{13}[/tex].

Then, Isaacs share is [tex]8x[/tex], so [tex]8\cdot\frac{32}{13}=20\frac{9}{13}[/tex]

Hope it helps!!

Answer:

Amir = 12 and Isaac = 20

Step-by-step explanation:

Given

[tex]Amir : Isaac = 5 : 8[/tex]

[tex]Munchkins = 32[/tex]

Required

Amount of munchkins given to each person

For Amir, the amount is calculated as:

[tex]Amir's = \frac{Amir}{Amir + Isaac} * Munchkins[/tex]

[tex]Amir's = \frac{5}{5+8} * 32[/tex]

[tex]Amir's = \frac{5}{13} * 32[/tex]

[tex]Amir's = \frac{5 * 32}{13}[/tex]

[tex]Amir's = \frac{160}{13}[/tex]

[tex]Amir's \approx 12[/tex]

For Isaac, the amount is calculated as:

[tex]Isaac's = \frac{Isaac}{Amir + Isaac} * Munchkins[/tex]

[tex]Isaac's = \frac{8}{5 + 8} * 32[/tex]

[tex]Isaac's = \frac{8}{13} * 32[/tex]

[tex]Isaac's = \frac{8 * 32}{13}[/tex]

[tex]Isaac's = \frac{256}{13}[/tex]

[tex]Isaac's \approx 20[/tex]

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