Surcharge and base price of additional price

Question

united express a national delivery service, charges a base price for overnight delivery pakages weighing 1 pound or less and a surcharge for each additional pound. a customer is billed $33.00 for shipping a 7 pound package and $74.25 for a 22 pound package. find base price and surcharge for each additional price.

Answer 1

Let B = base price for 1 pound or less  

Let S = surcharge for each additional pound over 1 

 

So the Cost is equal to S*(Pounds - 1) + B

 

$33.00 for 7 pounds  ==>  33.00 = S*(7-1) + B = 6*S + B  

$74.25 for 22 pounds  ==>  74.25 = S*(22-1) + B = 21*S + B  

 

Subtract the top equation from the bottom one to cancel the B's and get 

 

41.25 = 15*S 

S = 2.75  

 

Plug this value for S in to the 1st equation and solve for B  

 

33.00 = 6*(2.75) + B = 16.50 + B  

B = 16.50  

 

So the base charge is $16.50 and the surcharge is $2.75 for each additional pound  

 

Check:  7 pounds  ==>  C = 6*2.75 + 16.50 = 16.50 + 16.50 = $33.00

           22 pounds  ==>  C = 21*2.75 + 16.5 = 57.75 + 16.50 = $74.25