Question

A coin bank has 250 coins, dimes and quarters, worth $\$39.25$. How many of each type of the coins are there?

Answer 1

Hint: The worth of 1 dime is $\$0.1$ and the worth of 1 quarter is $\$0.25$. And we have given the total worth of all the 250 coins which is equal to $\$39.25$. Now, let us assume the number of dime coins in the coin bank are x then the number of quarter coins are $250-x$. Then we multiply x number of dime coins by $\$0.1$ and multiply $250-x$ number of quarter coins by $\$0.25$ and then we add these two multiplications and at last will equate this addition to $\$39.25$.

Complete step-by-step answer:
There are 250 coins in a coin bank. And there are two types of coins (i.e. dimes and quarters). Also, the total worth of 250 coins is given as $\$39.25$.
The worth of one dimes is given as:
$1\text{dime}=\$0.1$
And the worth of one quarter is given as:
$1\text{quarter}=\$0.25$
Let us assume x number of dimes are there in the coin bank then the number of quarters becomes $250-x$. Now, worth of x dimes is equal to:
$x\left( \$0.1\right)=\$0.1x$ ………. (1)
And worth of $\left( 250-x \right)$ quarters is equal to:
$\left( 250-x \right)\left( \$0.25\right)=\$0.25\left(250-x\right)$ …………….. (2)
Adding eq. (1) and (2) we get,
$\$0.1x+\$0.25\left(250-x\right)$
Equating the above addition to $\$39.25$ we get,
$\$0.1x+\$0.25\left(250-x\right)=\$39.25$
The $\$$ sign will be cancelled out from both the sides of the above equation and we get,
$\begin{align}
  & 0.1x+0.25\left( 250 \right)-0.25x=39.25 \\
 & \Rightarrow 0.1x+62.50-0.25x=39.25 \\
\end{align}$
Solving the x terms on one side of the equation and constant terms on the other side of the equation and we get,
$\begin{align}
  & \Rightarrow -0.15x=39.25-62.5 \\
 & \Rightarrow -0.15x=-23.25 \\
\end{align}$
Now, the negative sign will be cancelled out on both the sides and we get,
$0.15x=23.25$
Dividing 0.15 on both the sides of the equation we get,
$\begin{align}
  & x=\dfrac{23.25}{0.15} \\
 & \Rightarrow x=155 \\
\end{align}$
From the above, we have found that 155 coins are the dimes and the quarters are the subtraction of x from 250 so the quarters equal to:
$250-155=95$
Hence, we got the number of quarters as 95 and dimes as 155.

Note: To solve the above problem, you should know what the worth of a dime and a quarter is otherwise you cannot solve this problem. Also, make sure you won’t make any calculation mistakes in this problem because you can see the addition and subtraction of decimals so the possibility of making such mistakes is pretty high.