Question

Shane has some quarters and dimes. He has 34coins worth a total of $6.10 . How many of each type of coin does he have?

Answer 1

Given

He has 34 coins worth $6.10

Let the number of quarters he has be x and the number of dimes hes has be y

He has 34 coins implying:

`x\text{ + y = 34}`

From conversion rates, we have

`\begin{gathered} 4\text{ quarters = 1 dollar} \\ 10\text{ dimes = 1 dollar} \\ 1\text{ quarter = 0.25 dollars} \\ 1\text{ dime = 0.1 dollars} \end{gathered}`

Hence, we can write:

`0.25x\text{ + 0.1y = 6.10}`

To find x and y, we have to solve the equations simultaneously

`\begin{gathered} x\text{ + y = 34} \\ 0.25x\text{ + 0.1y = 6.10} \end{gathered}`

From the first equation:

`\begin{gathered} x\text{ + y = 34} \\ x\text{ = 34 -y} \end{gathered}`

Substituting into the second equation and solving for y:

`\begin{gathered} 0.25(34\text{ -y) + 0.1y = 6.10} \\ 8.5\text{ - 0.25y + 0.1y = 6.10} \\ \text{Collect like terms} \\ -0.15y\text{ = 6.1 - 8.5} \\ -0.15y\text{ = }-2.4 \\ Divide\text{ both sides by -0.15} \\ y\text{ = }16 \end{gathered}`

Substituting to find x:

`\begin{gathered} x\text{ = 34 - y} \\ \text{ = 34 - 16} \\ =\text{ }18 \end{gathered}`

We can conclude that Shana has 18 quarters and 16 dimes