Question

$\text{A baker buys enough supplies to bake 3 cakes,}\text{each weighing half a pound. Later, he decides}\text{to bake a different batch of cakes using the same}\text{supplies. The new batch of cakes has atleast one}\text{cake weighing}\frac{1}{2}\text{lb, one cake weighing}\frac{1}{4}\text{lb}\text{and another cake weighing}\frac{1}{8}\text{lb. Keeping the}\text{number of cakes as low as possible, find the}\text{correct line plot for the new batch of cakes.}$

• A. Plot A
• B. Plot B
• C. Plot C
• D. None of the above

Answer 1

The correct option is C Plot C

$Originalbatchofcakes:$

$\text{Total number of cakes}=3$
$\text{Weight of each cake}=\frac{1}{2}\text{lb}$
$⟹\text{Total weight of the cakes}=\frac{1}{2}\text{lb}+\frac{1}{2}\text{lb}+\frac{1}{2}\text{lb}=\frac{3}{2}\text{lb}$

$Newbatchofcakes:$
$\text{Total weight of the cakes}=\frac{3}{2}\text{lb}$
$\frac{3\times 4}{2\times 4}=\frac{12}{8}$
$⟹\frac{12}{8}\text{is an equivalent fraction of}\frac{3}{2}$

$\text{So, total weight of the cakes}=\frac{3}{2}\text{lb}=\frac{12}{8}\text{lb}$

$\text{Similarly,}\frac{1}{2}=\frac{1\times 4}{2\times 4}=\frac{4}{8}$

$\frac{1}{4}=\frac{1\times 2}{4\times 2}=\frac{2}{8}$

$\text{So, the weight of the three types of cakes}\text{will be}\frac{4}{8}\text{lb,}\frac{2}{8}\text{lb and}\frac{1}{8}\text{lb.}$

$\text{Now, to keep the number of cakes as low}\text{as possible, the baker has to make more}\text{of the heavier cakes.}$

$\text{If the baker makes 3 cakes, each weighing}\frac{4}{8}\text{lb, she would get:}$

$\frac{12}{8}\text{lb}=3\times \frac{4}{8}\text{lb}$

$\text{So, if 3 cakes, each weighing}\frac{4}{8}\text{lb, are made,}\text{there would not be any}\text{supplies left to make}\text{the other types of}\text{cakes.}$

$\text{Now, if the baker was to make 2 cakes,}\text{each weighing}\frac{4}{8}\text{lb, she would get:}$

$\frac{12}{8}\text{lb}=(2\times \frac{4}{8}\text{lb})+(1\times \frac{2}{8}\text{lb})+(2\times \frac{1}{8}\text{lb})$

$=(2\times \frac{1}{2}\text{lb})+(1\times \frac{1}{4}\text{lb})+(2\times \frac{1}{8}\text{lb})$

$\text{So, satisfying all the conditions, we get}\text{the new batch of cakes as:}$

$\text{Weight of the cake}$	$\frac{1}{2}\text{lb}$	$\frac{1}{4}\text{lb}$	$\frac{1}{8}\text{lb}$
$\text{Number of cakes}$	$2$	$1$	$2$

$\text{Plotting this data on a line plot, we get:}$


$\therefore \text{Plot C is the correct line plot representing}$ $\text{the new batch of cakes.}$