Question

Leah has $28$ more marbles than Dan. $\frac{1}{3}$ of Leah’s marbles is equal to $\frac{4}{5}$ of Dan’s marbles. Find the number of marbles that Leah has.

Answer 1

Finding the number of marbles Leah has:

Given, Leah has $28$ more marbles than Dan.

$\frac{1}{3}$ of Leah’s marbles = $\frac{4}{5}$ of Dan’s marbles.

Let $\mathrm{L}$ be the number of marbles with Leah and $\mathrm{D}$ be the number of marbles with Dan.

If Leah has $28$ more marbles than Dan,

$\Rightarrow L=D+28$

Also, if $\frac{1}{3}$ of Leah’s marbles is equal to $\frac{4}{5}$ of Dan’s marbles,

$\Rightarrow \frac{1}{3}L=\frac{4}{5}D$

Now substituting $L$ as $D+28$ in the above equation we get,

$$\begin{gathered} \frac{1}{3}\left(D+28\right)=\frac{4}{5}D \\ \Rightarrow 5\left(D+28\right)=12D \\ \Rightarrow 5D+140=12D \\ \Rightarrow 140=12D-5D \\ \Rightarrow 140=7D \\ \Rightarrow D=\frac{140}{7} \\ \Rightarrow D=20 \end{gathered}$$

Now substituting the value of $D$ as $20$ in $L=D+28$,

$$\begin{gathered} L=20+28 \\ L=48 \end{gathered}$$

Therefore, the number of marbles with Leah is $48$.