how to write a piecewise function from a word problem?

Question

a moving company charges according to the weight of boxes packed. if the total boxes weight is 10 pounds and under, the company charges $20. if the boxes weigh between 10 and up to 50 pounds, the company charges $35. if the total weight is over 50 pounds, the company charges $40, plus an additional $2 for each pound.

Write a piecewise function that describes what the moving company charges.

Answer 1

Let x be the weight of boxes. You have 3 regions to consider, x ≤ 10, 10< x ≤ 50, and 50 < x.

f(x) is the cost function and its output is dollars:

{ 20 if x ≤ 10

f(x) = { 35 if 10 < x ≤ 50

{ 2x-60 if 50 < x

For the last part (2x - 60) I assumed you meant additional $2 for each additional pound over 50.

That works out like this: x-50 = number of additional pounds, 40 is the "base" charge for 50 pounds and up; so we get 2(x-50)+40 = 2x-100+40 = 2x-60. Notice that if you plug in 50 pounds you get 2*50-60 = 40, which is the cost for a 50 pound move.