Question

In dimes and nickels, Chelsea has a total of $2.55 in her pocket. If she has six more nickels than dimes, how many of each coin does she have?

Answer 1

Let x be the number of dimes Chelsea has; since she has 6 more nickels than dimes this means that the number of nickels can be express as:

`x+6`

Now, we know that in total she has 2.55 and that the dimes are worth $0.1 and the nickels are worth $0.05, then we have the equation:

`0.1x+0.05(x+6)=2.55`

Solving for x we have:

`\begin{gathered} 0.1x+0.05(x+6)=2.55 \\ 0.1x+0.05x+0.3=2.55 \\ 0.15x=2.55-0.3 \\ 0.15x=2.25 \\ x=(2.25)/(0.15) \\ x=15 \end{gathered}`

Hence Chelsea has 15 dimes.

To determine the number of nickels we plug the value of x in the expression for the number of nickels, then we have:

`15+6=21`

Hence Chelsea has 21 nickels

Therefore we conclude that Chelsea has 15 dimes and 21 nickels.