Question

Cynthia has 52 coins in her piggy bank. these coins are nickels and quarters. the value of these coins is $9. how many nickels are in the bank? how many quarters are in the bank?

Answer 1

Let there are x number of nickels and y number of quarters.

Total coins are 52, so first equation is,

`\begin{gathered} x+y=52 \\ y=52-x \end{gathered}`

The worth of nckel is 0.05$ and worth of quarter is 0.25$.

The worth for the nickels and quarter is $9. So the second equation is,

`0.05x+0.25y=9`

Substitute the value of y in the equation to obtain the value of x.

`\begin{gathered} 0.05x+0.25(52-x)=9 \\ 0.05x+13-0.25x=9 \\ x=(-4)/(-0.20) \\ =20 \end{gathered}`

Substitute 20 for x in the equation y=52-x to obatin the value of y.

`\begin{gathered} y=52-20 \\ =32 \end{gathered}`

So number of nickels is 20 and number of quarters is 32.