Problem leading simple equations A sum of Rs. 8.85 is made up of 124 coins which are either 10 paisa coins or 5 paisa coins ; how many coins are there each Note : Rs. 1 = 100 paisas

1 RS = 100 paisas, so 8.85 RS = 885 paisas

885 paisas is made up of 124 coins, either 10 paisa coins or 5 paisa coins

Let x = the number of 10 paisa coins and y = the number of 5 paisa coins

then $124 = x + y$, so $x = 124 - y$

885 paisas = the number of 10 paisa coins * 10 (what they are worth) + the number of 5 paisa coins * 5 (what they are worth)

$ \begin{align} 885 &= 10x + 5y \\\ &= 10 (124 - y) + 5y \quad\quad(\text{ substituting in }x = 124 - y )\\\ &= 1240 - 10y + 5y \\\ &= 1240 - 5y \\\ -355 &= -5y \\\ 71 &= y \end{align} $

Since: $124 - y = x$

$\begin{align} 124 - 71 &= x \\\ 53 &= x \end{align} $

So there are 53 10-paisa coins and 71 5-paisa coins.

Check:

$\begin{align} 10x + 5y &= 10(53) + 5(71) \\\ &= 530 + 355 \\\ &= 885 \quad \checkmark \end{align} $