Final answer:
There are approximately 47 quarters and 81 dimes in the collection.
Step-by-step explanation:
Let's use algebra to solve this problem:
Let's assume that the number of quarters is 'x', which means the number of dimes would be 'x + 34'.
The value of each quarter is $0.25, and the value of each dime is $0.10. So, the value of the quarters would be 0.25x, and the value of the dimes would be 0.10(x + 34).
According to the problem, the total value of the coins is $19.85. So, we can set up the following equation:
0.25x + 0.10(x + 34) = 19.85
Simplifying the equation:
0.25x + 0.10x + 3.4 = 19.85
Combining like terms:
0.35x + 3.4 = 19.85
Subtracting 3.4 from both sides:
0.35x = 16.45
Dividing both sides by 0.35:
x = 16.45 / 0.35
x ≈ 47
So, there are approximately 47 quarters and 47 + 34 = 81 dimes in the collection.