Answer:
The number of each coin she have are <u>17 dimes</u> and <u>14 nickels</u>.
Step-by-step explanation:
Given:
A coin collector has 31 dimes and nickels with a total face value of $2.40.
Now, to find each does she have.
Let the number of dimes be .
Let the number of nickels be .
So, total number of coins are:
<em><u>Value of a dime = 10 cents</u></em>
<em><u>Value of a nickel = 5 cents</u></em>
<em><u>Total face value = 240 cents </u></em>
(1$ = 100 cents. $2.40×100 =240 cents)
Now, total value of coins:
Putting the equation (1) in the place of :
<em>Moving variables on one side and the numbers on other:</em>
<em>Dividing both sides by 5 we get:</em>
The number of nickels = 14.
Now, putting the value of in equation (1) we get:
<em>Subtracting both sides by 14 we get:</em>
The number of dimes = 17.
Therefore, the number of each coin she have are 17 dimes and 14 nickels.