a convention manager finds that she has $1410 made up of twenties and fifties. with a total of 48 bills, how many 50 dollar bills doe she have?
Ah, the convention manager is in the mood for a money mystery! Let's do some math while keeping it light-hearted, shall we?
Let's call the number of twenty-dollar bills "T" and the number of fifty-dollar bills "F." Since the manager has a total of 48 bills, we can create an equation to represent this situation:
T + F = 48
Now, let's bring the value of the bills into the equation, where the total amount is $1410:
20T + 50F = 1410
Now, let's have a little fun solving this mystery!
First, let's solve the first equation for T:
T = 48 - F
Now, substitute this into the second equation:
20(48 - F) + 50F = 1410
All right, now we're cooking! Let's simplify this equation:
960 - 20F + 50F = 1410
Combine like terms:
30F = 450
Almost there! Divide both sides of the equation by 30:
F = 15
Ah, jackpot! The convention manager has 15 fifty-dollar bills!
So, to answer your question, the convention manager has 15 fifty-dollar bills.
Now that we've solved the mystery, let's twist it around and make the manager the detective in search of a great punchline!
Let's solve this step-by-step:
Let's assume the number of fifty-dollar bills is "x"
The remaining bills, which are all twenty-dollar bills, would be 48 - x.
The value of the fifty-dollar bills would be 50 * x, and the value of the twenty-dollar bills would be 20 * (48 - x).
According to the given information, the total value of the bills is $1410.
So, we can set up the equation:
50x + 20(48 - x) = 1410
Now, let's simplify and solve the equation:
50x + 960 - 20x = 1410
Combining like terms:
30x + 960 = 1410
Subtracting 960 from both sides:
30x = 450
Dividing both sides by 30:
x = 15
Therefore, the convention manager has 15 fifty-dollar bills.
I hope this helps!
To determine the number of fifty-dollar bills the convention manager has, we can use a system of equations. Let's say she has x twenties and y fifties.
Given that she has a total of 48 bills, we can write the equation:
x + y = 48 ----(Equation 1)
The sum of the amount in twenties (20x) and the amount in fifties (50y) should equal $1410. This can be represented by the equation:
20x + 50y = 1410 ----(Equation 2)
Now we can solve this system of equations to find the values of x and y.
We can rearrange Equation 1 to solve for x:
x = 48 - y ----(Equation 3)
Substitute Equation 3 into Equation 2:
20(48 - y) + 50y = 1410
960 - 20y + 50y = 1410
30y = 1410 - 960
30y = 450
Divide both sides by 30 to isolate y:
y = 450 / 30
y = 15
Therefore, the convention manager has 15 fifty-dollar bills.