Question

I have 20 more nickels than I have dimes. If the sum of money I have is 8.50 dollars, how many coins of each type do I have?

Answer 1

Hint: First of all convert all the nickels, dimes and dollars into cents by using the relations: 1 nickel = 5 cents, 1 dime = 10 cents and 1 dollar = 100 cents. Now, assume that there are x dimes and (20 + x) nickels. Form a linear equation in one variable (x) using the information given and solve for the value of x to get an answer.

Complete step by step solution:
Let us assume that the number of dimes is x, so according to the question which states that there are 20 more nickels than the dimes, we must have (20 + x) nickels. As we can see that the nickel, dime and dollars are different units of the currency so we need to convert them into a particular unit. Here we are going to convert them into cents by using the relations: 1 nickel = 5 cents, 1 dime = 10 cents and 1 dollar = 100 cents. So we have,
$\Rightarrow $ x dimes = 10x cents, (20 + x) nickel = 5(20 + x) cents and 8.50 dollars = 850 cents.
According to the question we must have the following relation:
$\begin{align}
  & \Rightarrow 10x+5\left( 20+x \right)=850 \\
 & \Rightarrow 10x+100+5x=850 \\
 & \Rightarrow 15x=850-100 \\
 & \Rightarrow 15x=750 \\
\end{align}$
Dividing both the sides with 15 we get,
$\therefore x=50$
So, we get $\left( 20+x \right)=70$
Therefore, there are 50 dimes and 70 nickels.

Note: Remember that here we are not dealing with Indian currency to INR is of no use here. You must know the relationship between dollars – cents, dollars – cents, dimes – cents and nickel – cents to solve the above question. Do not forget to find the number of nickels in the end as sometimes in a hurry we just calculate the value of x and say it as our answer.