Write an equation that gives the total cost of shipping a package as a function of the weight of the package

Question

A delivery service charges a base price of $15.50 for an overnight delivery of packages plus an extra charge of each pound the package weights. A customer is billed $22.85 for a shipping of 3 lb packages and $40 for shipping of 10 lb.

Answer 1

For the 3 lb package, let's subtract the $15.50 base price from the total bill of $22.85.

 

22.85 - 15.50 = $7.35

 

If the total weight of the package is 3 lb, then the price per lb is 7.35/3 = $2.45.

 

Likewise, if we deduct the base price for the 10 lb package from the total bill of $40, then we have:

 

40 - 15.50 = $24.50.

 

If the package is 10 lb, then the price per lb is 24.50/10 = $2.45.

 

Our equation would then be:

 

c(x) = 15.50 + 2.45x

 

where c is the total shipping cost and x represents the weight of the package.