Question

a jar of nickels and dimes contains $5.45. There are 8 more dimes than nickels. How many of each are there?

Answer 1

Let the number of dimes = x

And the number of nickels = y

There are 8 more dimes than nickels.

So, x = y + 8

The jar of nickels and dimes contains $5.45

So, the total amount of money = 545 cents

dime = 10 cents

nickel = 5 cents

so, 10x + 5y = 545

so, we have the following system of equations:

`\begin{gathered} x=y+8\rightarrow(1) \\ 10x+5y=545\rightarrow(2) \end{gathered}`

Substitute with x from equation (1) into equation (2) then solve for y

`\begin{gathered} 10(y+8)+5y=545 \\ 10y+80+5y=545 \\ 15y=545-80 \\ 15y=465 \\ \\ y=(465)/(15)=31 \\ x=31+8=39 \end{gathered}`

So, the number of dimes = 39

The number of nickels = 31