Question

A retailer charges a flat handling fee of $5.00, plus $0.75 per quarter pound, to ship an item. Bailey pays $9.50 to have an item shipped from the retailer. What is the weight of the item?

Answer 1

See a solution process below:

Explanation:

The formula for the charge is:

`c = f + rw`

Where:

• `c` is the total cost: $9.50 for this problem.

• `f` is the fixed cost: $5.00 for this problem

• `r` is the rate for the variable charge: `($0.75)/(0.25"lb")` or `($3.00)/"lb"` for this problem,

• `w` is the weight being shipped. What we are solving for in this problem.

Substituting and solving for `w` gives:

`$9.50 = $5.00 + ($3.00)/"lb"w`

`$9.50 - color(red)($5.00) = $5.00 - color(red)($5.00) + ($3.00)/"lb"w`

`$4.50 = 0 + ($3.00)/"lb"w`

`$4.50 xx color(blue)("lb")/(color(red)($)color(red)(3.00)) = ($3.00)/"lb"w xx color(blue)("lb")/(color(red)($)color(red)(3.00))`

`(color(red)(cancel(color(black)($)))4.50) xx color(blue)("lb")/(cancel(color(red)($))color(red)(3.00)) = (color(red)(cancel(color(black)($3.00))))/color(blue)(cancel(color(black)("lb")))w xx cancel(color(blue)("lb"))/(cancel(color(red)($)color(red)(3.00)))`

`4.50/3.00color(blue)("lb") = w`

`1.5"lb" = w`

`w = 1.5"lb"`

The weight of the item Bailey shipped was `color(red)(1.5"lb")`