Question

$\text{A group of friends share a pizza such that}\frac{3}{4}\text{ths}\text{of the pizza is shared equally by the girls while}\text{the remaining}\frac{1}{4}\text{th is shared equally by the boys.}\text{What should be the number of boys and girls}\text{in the group such that each person gets an equal}\text{share of the pizza?}$

• A. Girls = 3 ; Boys = 4
• B. Girls = 4 ; Boys = 3
• C. Girls = 6 ; Boys = 2
• D. Girls = 2 ; Boys = 6

Answer 1

The correct option is C Girls = 6 ; Boys = 2

The fraction of pizza shared between the girls can be calculated as:


The fraction of pizza shared between the boys can be calculated as:


$Case1:\text{Girls = 3 ; Boys = 4}$

$\text{Portion of pizza that each girl gets}=\frac{3}{4}÷3=\frac{3}{4}\times \frac{1}{3}=\frac{3\times 1}{4\times 3}=\frac{1}{4}$

$\text{Portion of pizza that each boy gets}=\frac{1}{4}÷4=\frac{1}{4}\times \frac{1}{4}=\frac{1\times 1}{4\times 4}=\frac{1}{16}$

$⟹\text{Portions are not equal.}$

$Case2:\text{Girls = 4 ; Boys = 3}$

$\text{Portion of pizza that each girl gets}=\frac{3}{4}÷4=\frac{3}{4}\times \frac{1}{4}=\frac{3\times 1}{4\times 4}=\frac{3}{16}$

$\text{Portion of pizza that each boy gets}=\frac{1}{4}÷3=\frac{1}{4}\times \frac{1}{3}=\frac{1\times 1}{4\times 3}=\frac{1}{12}$

$⟹\text{Portions are not equal.}$

$Case3:\text{Girls = 6 ; Boys = 2}$

$\text{Portion of pizza that each girl gets}=\frac{3}{4}÷6=\frac{3}{4}\times \frac{1}{6}=\frac{3\times 1}{4\times 6}=\frac{1}{4\times 2}=\frac{1}{8}$

$\text{Portion of pizza that each boy gets}=\frac{1}{4}÷2=\frac{1}{4}\times \frac{1}{2}=\frac{1\times 1}{4\times 2}=\frac{1}{8}$

$⟹\text{Portions are equal.}$

$Case4:\text{Girls = 2 ; Boys = 6}$

$\text{Portion of pizza that each girl gets}=\frac{3}{4}÷2=\frac{3}{4}\times \frac{1}{2}=\frac{3\times 1}{4\times 2}=\frac{3}{8}$

$\text{Portion of pizza that each boy gets}=\frac{1}{4}÷6=\frac{1}{4}\times \frac{1}{6}=\frac{1\times 1}{4\times 6}=\frac{1}{24}$

$⟹\text{Portions are not equal.}$
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$\therefore \text{If the number of girls is 6 and the number}$ $\text{of boys is 2, then each member of the}\text{group would get an equal fraction of the}\text{pizza as their share.}$