Question

I have some five-rupee coins and some two-rupee coins. The number of two-rupee coins is twice the number of five-rupee coins. The total money i have is $108$ rupees. How many five-rupee coins do i have ?

Answer 1

Step 1: Identifying given data and simplifying.

Let the number of five-rupee coins be $\mathrm{x}$

Then the number of two-rupee coins will be $2\mathrm{x}$

Amount in five-rupee coin will be $5\mathrm{x}$ rupees and

Amount in two-rupee coin will be $\left[2\left(2\mathrm{x}\right)=4\mathrm{x}\right]$ rupees.

Step 2: Finding the value of $\mathrm{x}$

Now according to given condition,

$5\mathrm{x}+4\mathrm{x}=108$

$$\begin{gathered} \Rightarrow 9\mathrm{x}=108 \\ \Rightarrow \mathrm{x}=\frac{108}{9} \\ \Rightarrow \mathrm{x}=\frac{{\displaystyle \stackrel{12}{\cancel{108}}}}{\cancel{9}} \\ \Rightarrow \mathrm{x}=12 \end{gathered}$$

So, I have $12$ five-rupee coins.