Final answer:
To solve this problem, you can set up a system of equations to represent the number of dimes and quarters. By solving these equations, you can find the values of 'd' and 'q'. In this case, there are 73 dimes and 27 quarters.
Step-by-step explanation:
To solve this problem, you can set up a system of equations. Let's say the number of dimes is 'd' and the number of quarters is 'q'. We know that the total number of coins is 100, so we can write the equation:
d + q = 100
We also know that the total value of the coins is $14.05. Since each dime is worth 10 cents (0.10 dollars) and each quarter is worth 25 cents (0.25 dollars), we can write another equation to represent the total value:
0.10d + 0.25q = 14.05
Now we can solve these equations to find the values of 'd' and 'q'.
Simplifying the first equation, we get:
d = 100 - q
Substituting this into the second equation, we have:
0.10(100 - q) + 0.25q = 14.05
Expanding and simplifying, we get:
10 - 0.10q + 0.25q = 14.05
Combining like terms, we have:
0.15q = 4.05
Dividing both sides by 0.15, we find:
q = 27
Substituting this back into the first equation, we can calculate:
d = 100 - 27
d = 73
Therefore, there are 73 dimes and 27 quarters.