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

Answer:

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

Step-by-step 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.