Question

Sumanta has $\$4.20$ in nickels and dimes in her piggy bank. She has twice as many nickels as dimes. How many coins of each type does she have?

Short answer

Sumanta has $21$dimes and $42$nickels in her piggy bank.

Step-by-step solution

Step 1. Given information.

Consider the given question,

Sumanta has twice as many nickels as dimes.

We know, the value of a dime is $\$0.1$and value of nickel is $\$0.05$. The total value of all the coins is $\$4.2$.

Assume nand dto be the number of nickels and dimes.

$n=2d$

Make the table,

Step 2. Form the equation.

Consider the table, we can see,

$$\begin{gathered} 0.1d+0.05\left(2d\right)=4.2 \\ 0.1d+0.1d=4.2 \\ 0.2d=4.2 \\ d=21 \end{gathered}$$

Then,

$$\begin{gathered} n=2\left(21\right) \\ n=42 \end{gathered}$$

Therefore, Sumanta has $21$dimes and $42$nickels in her piggy bank.