Question

A woman has three times as many five rupee coins as she has two rupee coins. Also, the total amount with the woman is $Rs\,85$. How many coins of each denomination does she have?

Answer 1

Hint: We are given a word problem that requires us to formulate an algebraic equation and then solve it to get to the required answer. So, we first consider the number of two rupee coins as a variable and then express the number of five rupee coins in terms of the same variable. Then, we find the total amount of money with the woman and equate it to $Rs\,85$ to form an equation.

Complete step by step solution:
Let us consider the number of two rupee coins as $x$.
Then, the number of five rupee coins is $3x$.
Now, we calculate the amount in each denomination.
So, the total amount in two rupee coins $ = 2x$
The total amount in five rupee coins $ = 5\left( {3x} \right) = 15x$
Now, the total amount with the woman is given to us as $Rs\,85$.
So, we have, $2x + 15x = Rs\,85$
Now, we have to solve the equation to find the value of x in the equation. So, we get,
$ \Rightarrow 17x = Rs\,85$
Dividing both sides of equation by $17$, we get,
$ \Rightarrow x = \dfrac{{85}}{{17}}$
Cancelling common factors in numerator and denominator, we get,
$ \Rightarrow x = 5$
So, the value of x is $5$.
Hence, the number of two rupee coins is $5$. Also, the number of five rupee coins is $15$.

Note:
The above-mentioned method can be remembered as a complete process for solving these types of questions. Be careful with the language while attending these types of questions, because there are many questions which may confuse you with the tricky and typical language. These types of questions are easy to solve when you are writing an exam as it takes less time to solve when you are thorough with this concept and have practised ample amount of questions. Method of transposition involves doing the same mathematical operation on both sides of the equation so that it remains unchanged.