Question

in a coin Bank , there are 104 dime and quarters worth a total of $14 . how many of each type of coins are in the bank .

Answer 1

we have the following:

We can solve the question by a system of equations, like this

let x, number of dime = $0.10

let y, number of quarter = $0.25

$\begin{gathered} x+y=104\rightarrow x=104-y \\ 0.10x+0.25y=14 \\ 0.10\cdot(104-y)+0.25y=14 \\ 10.4-0.1y+0.25y=14 \\ 0.15y=14-10.4 \\ y=\frac{3.6}{0.15}=24 \end{gathered}$

now, for x:

$\begin{gathered} x=104-24 \\ x=80 \end{gathered}$

therefore, there are 24 quarters and 80 dimes, in total 104 coins and represent $14