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

Answer:

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

Step-by-step 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:

$\frac{y}{2} =\frac{x}{3}$

On solving we get:

$y=\frac{2x}{3}$.........(2)

$\frac{x}{2} =\frac{z}{5}$

On solving we get:

$\frac{5x}{2} =z$.........(3)

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

$x+\frac{2x}{3} +\frac{5x}{2}=500$

On solving the equation we get:

$\frac{6x+4x+15x}{6}=500$

$\frac{25x}{6} =500$

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:

$y=\frac{2\times 120}{3}$

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:

$Dimes = \ 0.10 \times 120=\ 12.$

$Nickels = \ 0.05 \times 80=\ 4.$

$Quarters =\ 0.25 \times 300=\ 75.$

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.