A piggy bank contains nickels and dimes. There are 160 total coins valuing $10.50. Think about a system of equations that can be used to represent the number of nickels and dimes and then think through using substitution to solve the system of equations. How many nickels are in the piggy bank?

Question

anonymous · Answer

Let $n$ and $d$ represent the number of nickels and dimes, respectively.

There are 160 total coins made up of nickels and dimes, so you have $n+d=160$.

The value of a nickel is $0.05, so the portion of the total value in the bank in nickels is $0.05n$. Similarly, a dime is valued at $0.10, so you have $0.10d$. A total of $10.50 in the bank tells you that you have $0.05n+0.10d=10.50$.

So you have the system
$$\begin{cases}n+d=160\0.05n+0.10d=10.50\end{cases}$$