Answer: the coin bank has 50 dimes and 16 quarters.
Step-by-step explanation:
The worth of a dime is 10 cents. Converting to dollars, it becomes
10/100 = $0.1
The worth of a quarter is 25 cents. Converting to dollars, it becomes
25/100 = $0.25
Let x represent the number of dimes in the coin bank.
Let y represent the number of quarters in the coin bank.
A coin bank containing only dimes and quarters has 34 more dimes than quarters. This means that
x = y + 34
The total value of the coins is $9. This means that
0.1x + 0.25y = 9 - - - - - - - - - - - 1
Substituting x = y + 34 into equation 1, it becomes
0.1(y + 34) + 0.25y = 9
0.1y + 3.4 + 0.25y = 9
0.1y + 0.25y = 9 - 3.4
0.35y = 5.6
y = 5.6/0.35 = 16
x = y + 34 = 16 + 34
x = 50
