Final answer:
Susan has 33 nickels and 11 dimes. We derived this by setting up two equations based on the total number of coins and the ratio of nickels to dimes, then solved the equations simultaneously.
Step-by-step explanation:
To solve the problem, we need to create two equations based on the information given. We know the total number of coins (nickels and dimes) and the ratio between them. Let's denote the number of dimes as d and the number of nickels as n. The first equation results from the total number of coins, which is d + n = 44. The second equation is based on the ratio between nickels and dimes, stated as the number of nickels being three times the number of dimes, written as n = 3d.
Now we solve these two equations simultaneously. First, we substitute the value of n from the second equation into the first equation. Therefore, 3d + d = 44, which simplifies to 4d = 44. Dividing both sides of the equation by 4 gives us d = 11. Now that we have the number of dimes, we can find the number of nickels by plugging this value back into the second equation: n = 3 x 11, thus n = 33.
So, Susan has 33 nickels and 11 dimes in her collection.