United Express, a nationwide 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 $ 25 $25 for shipping a 7 7-pound package and $ 55 $55 for shipping a 22 22-pound package. Find the base price and the surcharge for each additional pound. Round answers to the nearest thousandth (to three decimal places).

Question

contestada

Respuesta :

mtosi17 mtosi17 · Answer 1 · 2020-06-05T02:26:17+02:00

Answer:

Base price: $13.

Surcharge: $2 per additional pound.

Step-by-step explanation:

The base price can be considered a constant, while the surcharge is a function of the additional weight of the package, over 1 pound.

Then, we can model this as a linear function, with additional weight as the independent variable.

[tex]f(x)=b+sx[/tex]

being b: base price, and s: surcharge for each additional pound.

The 7-pound package cost $25. The additional weigth in this case is 7-1=6 pounds.

The 22-pound package cost $55. The additional weigth is 21 pounds.

So we have the first point (6, 25):

[tex]f(6)=b+s(6)=25\\\\b=25-6s[/tex]

Then, for the second point (21, 55) we have:

[tex]b=25-6s\\\\f(21)=(25-6s)+s(21)=55\\\\25+(21-6)s=55\\\\15s=55-25=30\\\\s=30/15=2\\\\\\b=25-6(2)=25-12=13[/tex]

Then, the prices are:

Base price: $13.

Surcharge: $2 per additional pound.