United Express, a national package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each additional pound (or fraction thereof). A customer is billed $29.00 for shipping a 7 -pound package and $64.00 for a 27 -pound package. Find the base price and the surcharge for each additional pound.

The base charge = $18.5 and surcharge for each pound is = $1.75

Step-by-step explanation:

Solution:

- Denote:

Base charge = $x ... For for Weight ≤ 1 lbs

Additional charge = $y / unit pounds

- We are given that the customer is billed $29.00 for shipping a 7 -pound package. We can express this statement in terms of "x" and "y".

- The 1-pound out of 7 pounds will be charged with $x and remaining 6 additional pounds of weight will be charged "$y" for each unit of weight.

$x + (7 - 1) * $y = $29.00 ... Eq1

- Similarly for a receipt of $64.00 for a 27 -pound package. The 1-pound out of 27 pounds will be charged with $x and remaining 26 additional pounds of weight will be charged "$y" for each unit of weight.

$x + (27 - 1) * $y = $64.00 ... Eq2

- Now solve the two equations simultaneously by subtracting Eq1 from Eq2:

(26 - 6) * $y = $ (64 - 29)

20*$y = $35

y = 1.75

$x = 29 - 6*1.75

x = 18.5

- The base charge = $18.5 and surcharge for each pound is = $1.75