Final answer:
To find the number of quarters and pennies, we can set up a system of equations based on the total value and the total number of coins. By solving these equations, we find that Dustin has 18 quarters and 15 pennies.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's say the number of quarters is q and the number of pennies is p. We know that the total value of the coins is $4.65, so we can write the equation: 0.25q + 0.01p = 4.65. We also know that there are 33 coins, so we can write the equation: q + p = 33.
Now we can solve this system of equations. We can multiply the second equation by -0.25 to eliminate q: -0.25q - 0.25p = -8.25. Adding this equation to the first equation, we get: 0.25q + 0.01p + (-0.25q - 0.25p) = 4.65 + (-8.25). Simplifying, we get: -0.24p = -3.6. Dividing both sides by -0.24, we find that p = 15. Therefore, there are 15 pennies.
Substituting this value back into the second equation, we find that q + 15 = 33. Solving for q, we get q = 18. Therefore, there are 18 quarters.