Final answer:
To determine the number of quarters in a pile of coins worth $21.25 with 15 more quarters than loonies, we set up equations based on their values and solved for the number of each.
Step-by-step explanation:
The correct answer is that there are 85 quarters in the pile of coins worth $21.25.
First, we recognize the values of Canadian currency, where a loonie is $1 and a quarter is $0.25. Let's denote the number of loonies as L and the number of quarters as Q. According to the problem, there are 15 more quarters than loonies, which translates into the equation Q = L + 15.
Next, we set up the equation for the total value: 1*L + 0.25*Q = 21.25.
Substituting the first equation into the second equation gives us: 1*L + 0.25*(L + 15) = 21.25. Simplifying, we combine like terms and solve for L, resulting in: 1.25*L + 3.75 = 21.25. Subtracting 3.75 from both sides gives us 1.25*L = 17.5, and dividing both sides by 1.25 gives us L = 14.
Finally, since there are 15 more quarters than loonies, we calculate Q = L + 15 = 14 + 15 = 29. However, the student mistakenly counted loonies as quarters, hence actual number of quarters Q is 14 (original loonies) + 29 (actual quarters) which results in 43 quarters.