Question

There are some nickels dimes and quarters in a large piggy bank. For every two nickels there are three dimes. For every two dimes There are 5 Quarters. There are 500 coins total. How many nickels dimes and quarters are in the piggy bank. How much are the coins in the piggy bank worth.

Answer 1

The number of coins each are 120 dimes, 80 nickels and 300 quarters. And the coins worth dimes →$12, nickels →$4 and quarters →$75.

Explanation:

Given:

For every two nickels there are three dimes. For every two dimes There are 5 Quarters. There are 500 coins total.

Now, to find the number of nickels, dimes and quarters. And the coins worth.

Let the number of dimes be
`x`.

The the number of nickels be
`y`.

And the number of quarters be
`z`.

So, the number of total coins are:

`x+y+z=500`.........(1)

Now, as per given in question:

`(y)/(2) =(x)/(3)`

On solving we get:

`y=(2x)/(3)`.........(2)

`(x)/(2) =(z)/(5)`

On solving we get:

`(5x)/(2) =z`.........(3)

Now, in equation(1) substituting the equation (2) and(3) in the place of
`y\ and\ z` we get:

`x+(2x)/(3) +(5x)/(2)=500`

On solving the equation we get:

`(6x+4x+15x)/(6)=500`

`(25x)/(6) =500`

Multiplying both sides by 6 we get:

`25x=3000`

Dividing both sides by 25 we get:

`x=120.`

Number of dimes = 120.

Putting the value of
`x` in equation 2 we get:

`y=(2* 120)/(3)`

On solving we get:

`y=80.`

The number of nickels = 80.

Now, putting the value of
`x` and
`y` in equation 1 we get:

`120+80+z=500`

`200+z=500`

On solving we get:

`z=300`

The number of quarters = 300.

Now, the coins worth:

`Dimes = \$0.10 * 120=\$12.`

`Nickels = \$0.05 * 80=\$4.`

`Quarters =\$0.25 * 300=\$75.`

Therefore, the number of coins each are 120 dimes, 80 nickels and 300 quarters. And the coins worth dimes →$12, nickels →$4 and quarters →$75.