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?

Answer 1

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}.