A convention manager finds that she has $1410, made up of twenties and fifties. She has a total of 48 bills. How many fifty dollar bills does the manager have?

My answer is: 15
Is this correct?
Thanks.

It must be correct.

Let's solve the problem step by step:

1. Let's assign variables to the unknowns in the problem. Let t represent the number of twenties, and f represent the number of fifty-dollar bills.

2. According to the problem statement, the convention manager has a total of 48 bills. Therefore, we can write the equation: t + f = 48.

3. The total amount of money the manager has is $1410. Since each twenty-dollar bill is worth $20 and each fifty-dollar bill is worth $50, we can write the second equation: 20t + 50f = 1410.

4. To solve the system of equations, we can use a method called substitution. Rearrange the first equation to solve for t: t = 48 - f.

5. Now substitute the value of t in the second equation: 20(48 - f) + 50f = 1410.

6. Simplify the equation: 960 - 20f + 50f = 1410.

7. Combine like terms: 30f = 450.

8. Divide both sides of the equation by 30: f = 15.

Therefore, the convention manager has 15 fifty-dollar bills. Your answer is correct!