Question

Translate to a system of equations and solve:Whitney has a collection of nickels and dimes, with a total value of $5.40. The number of nickels is two less than four times the number of dimes. How many nickels and how many dimes does she have?

Answer 1

Let n and d be the number of nickels and dimes, respectively. Since the total values is $5.40, we can write

`0.05n+0.10d=5.40`

On the other hand, since the number of nickels is two less than four times the number of dimes, we have

`n=4d-2`

Then, we have the following system of equations:

`\begin{gathered} 0.05n+0.10d=5.40\ldots(a) \\ n=4d-2\ldots(b) \end{gathered}`

Solving by substitution method.

By substituting equation (b) into (a), we have

`0.05(4d-2)+0.10d=5.40`

By distributing 0.05 into the parenthesis, we have

`0.2d-0.1+0.10d=5.40`

and by combining similar terms, we have

`0.3d-0.1=5.40`

then, we have

`\begin{gathered} 0.3d=5.40-0.1 \\ 0.3d=5.30 \end{gathered}`

By dividing both sides by 0.3, we get

`\begin{gathered} d=(5.30)/(0.3) \\ d=17.666 \end{gathered}`