A post office always charges a flat one-time fee for any order. One time, Michael sent 35 letters and paid $26.00. The next time, he sent 18 letters and paid $14.10. How much does the post office charge to send one letter? What is the flat fee?
Let x be the charge for one letter and y be the flat fee.
For the first order, Michael sent 35 letters, so the total was 35*x + y = $26.00.
For the second order, Michael sent 18 letters, so the total was 18*x + y = $14.10.
We can multiply the second equation by -35 to eliminate y: -35*(18*x + y) = -35*$14.10.
This simplifies to -630*x - 35*y = -35*$14.10.
Now we can subtract the first equation from the second equation to eliminate y: (18*x + y) - (35*x + y) = $14.10 - $26.00.
This simplifies to -17*x = -$11.90.
Dividing both sides by -17 gives x = $0.70.
Substituting this back into the first equation gives 35*0.70 + y = $26.00.
This simplifies to 24.50 + y = $26.00.
Subtracting 24.50 from both sides gives y = $1.50. Answer: \boxed{1.50}.
To find out how much the post office charges to send one letter, we can set up a system of equations based on the given information.
Let's say the flat fee charged by the post office for one order is represented by the variable "x."
From the first scenario, we know that Michael sent 35 letters and paid $26.00. This can be written as:
35x = $26.00 -- equation (1)
From the second scenario, we know that Michael sent 18 letters and paid $14.10. This can be written as:
18x = $14.10 -- equation (2)
To find the value of "x," we can solve this system of equations.
Dividing both sides of equation (1) by 35:
x = $26.00 / 35
x = $0.74
So, the post office charges $0.74 to send one letter.
To find the flat fee, we can substitute the value of "x" into either equation (1) or (2). Let's use equation (1):
35 * $0.74 = $26.00
Therefore, the flat fee charged by the post office is $26.00.