Question

A coin collector has 31 dimes and nickels with a total face value of $2.40. (They are actually worth a lot more.) How many of each coin does she have?

Answer 1

The number of each coin she have are 17 dimes and 14 nickels.

Explanation:

Given:

A coin collector has 31 dimes and nickels with a total face value of $2.40.

Now, to find each does she have.

Let the number of dimes be
`x`.

Let the number of nickels be
`y`.

So, total number of coins are:

`x+y=31`

`x=31-y.............(1)`

Value of a dime = 10 cents

Value of a nickel = 5 cents

Total face value = 240 cents

(1$ = 100 cents. $2.40×100 =240 cents)

Now, total value of coins:

`10x+5y=240`

Putting the equation (1) in the place of
`x`:

`10(31-y)+5y=240`

`310-10y+5y=240`

`310-5y=240`

Moving variables on one side and the numbers on other:

`310-240=5y`

`70=5y`

Dividing both sides by 5 we get:

`14=y`

The number of nickels = 14.

Now, putting the value of
`y` in equation (1) we get:

`x+y=31`

`x+14=31`

Subtracting both sides by 14 we get:

`x=17.`

The number of dimes = 17.

Therefore, the number of each coin she have are 17 dimes and 14 nickels.