Question

The given line plot shows the amount of ice cream a group of people purchase. If all of them share the ice cream equally, how much ice cream will each person get?

• A. Share of each person is $1\frac{1}{63}lb$
• B. Share of each person is $9\frac{3}{14}lb$
• C. Share of each person is $1\frac{2}{64}lb$
• D. Share of each person is $9lb$

Answer 1

The correct option is A Share of each person is $1\frac{1}{63}lb$

Weight of ice cream (lb)	Frequency (Number of people)	Weight of ice cream (lb)
$\frac{1}{7}$	$3$	$3\times \frac{1}{7}=\frac{3\times 1}{7}=\frac{3}{7}$
$1\frac{1}{7}=\frac{(1\times 7)+1}{7}=\frac{8}{7}$	$4$	$4\times \frac{8}{7}=\frac{4\times 8}{7}=\frac{32}{7}$
$2\frac{1}{14}=\frac{(2\times 14)+1}{14}=\frac{29}{14}$	$2$	$2\times \frac{29}{14}=\frac{2\times 29}{14}=\frac{58}{14}$
	Total $=9$

Total amount of ice cream purchased $=\frac{3}{7}+\frac{32}{7}+\frac{58}{14}lb$
$\frac{3}{7},\frac{32}{7},$ and $\frac{58}{14}$ are unlike fractions. Convert them into like fractions by finding the equivalent fraction of $\frac{3}{7}$ and $\frac{32}{7}$ with denominator $14$.

$\frac{3}{7}=\frac{3\times 2}{7\times 2}=\frac{6}{14}$

$\frac{32}{7}=\frac{3\times 2}{7\times 2}=\frac{64}{14}$

So, total weight of ice cream purchased $=\frac{6}{14}+\frac{64}{14}+\frac{58}{14}=\frac{128}{14}lb$

Total number of people in the group $=3+4+2=9$
If all the purchased ice cream is distributed among the group equally, then share of each

person = Total amount of ice cream purchased $÷$ Number of people in the group
Share of each person $=\frac{128}{14}÷9$

By using the concept of keep change flip:
$\frac{128}{14}÷9=\frac{128}{14}\times \frac{1}{9}=\frac{128}{126}=\frac{64}{63}=1\frac{1}{63}lb$