Question

Jesse has 38 nickels and dimes. The number of nickels is 1 less than twice thenumber of dimes. How many of each coin does Jesse have?

Answer 1

`25\: nickels\: and\: 13\: dimes`

1) The best way to tackle this is to write a system of linear equations.

2) So we can write out the following:

`\begin{gathered} n+d=38 \\ n=2d-1 \end{gathered}`

So now, let's solve it via the Substitution Method, picking the 2nd equation and plugging it into the first one:

`\begin{gathered} (2d-1)+d=38 \\ 2d-1+d=38 \\ 3d-1=38 \\ 3d-1+1=38+1 \\ 3d=39 \\ (3d)/(3)=(39)/(3) \\ d=13 \end{gathered}`

3) Now, that we know how many dimes Jesse has, let's figure out how many nickels by plugging into one of those equations, (usually the simplest one) the number of dimes we have just found:

`\begin{gathered} n+d=38 \\ n+13=38 \\ n+13-13=38-13 \\ n=25 \end{gathered}`