A collection of 25 coins consists of nickels, dimes, and quarters. There are three times as many dimes as nickels and three more dimes than quarters. What is the total value of the collection in dollars and cents?
1 Answer
$3.65
Explanation:
Let
We know that
We know that there are three times as many dimes as nickels, which means our second equation is:
(Think: If there was 1 nickel there would be 3 dimes.)
We know that there are three more dimes than quarters so our third equation is:
(Think: If there were 3 quarters we would have 6 dimes.)
So we have three equations:
(1)
(2)
(3)
Solving (2) for
Solving (3) for
Taking these and substituting into (1) gives:
Adding 3 to both sides and doing the easy combination on the left:
Multiply through by 3:
Collect like terms:
Divide both sides by 7:
Know that
from (2):
from (3):
So 4 nickels, 12 dimes, and 9 quarters.
The value of the collection is
so $3.65.