Question

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

$0.70 per letter, $1.50 flat fee

Explanation:

Let x be the flat fee.

Let y be the cost of sending 1 letter.

Lets create 2 equations from those 2 instances.

First Instance: x + 35y = 26 - Equation 1

Second Instance: x + 18y = 14.1 - Equation 2

To find x and y , we can use elimination method in solving simultaneous equations.

Equation 1 - Equation 2

x - x + 35y - 18y = 26 - 14.1

17y = 11.9

y =
`(11.9)/(17) \\`

= $0.70

Now we substitute y into equation 1.

x + 35(0.70) = 26

x + 24.50 = 26

x = 26 - 24.50

= $1.50

From the above we know the post charges $0.70 per letter sent and charges $1.50 flat fee.