# If it costs .46 to mail each letter plus 3.67 for a box of envelopes to mail them all, how much will it cost to mail 23 letters

*print*Print*list*Cite

It costs $0.46 to mail a letter plus $3.67 for a box of envelopes. Find the cost of mailing 23 letters.

You could use a linear relationship to describe this situation. One way to represent a linear relationship is an equation in the form y=mx+b. Here y represents the output, x the input, b the y-intercept (the output when the input is zero) and m the slope (or the constant rate of change for the input variable.)

For our question, the output Cost depends on the input of the number of letters mailed. Let y be the total cost and x the number of letters. b is the cost if no letters are mailed and m is the cost per letter mailed.

b=3.67 since we have to buy the envelopes. m=.47 since this is the cost per mailing.

Thus y=.46x+3.67 is an equation we can use to model the given situation. Note that the values of x (the domain of the function) is nonnegative integers.

For x=23 we have y=(.46)(23)+3.67=14.25

--------------------------------------------------------------------------

The total cost for 23 letters is $14.25

------------------------------------------------------------------------

The easiest way to do this is to multiply the cost of the stamps times the number of letters. .46x23=10.58. Now add the cost of the envelopes. 10.58+3.67=14.25.

The total cost is $14.25