# 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? ##### 1 Answer Jul 4, 2018 See a solution process below: #### Explanation: The formula for the charge is: $c = f + r w$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))) $\frac{4.50}{3.00} \textcolor{b l u e}{\text{lb}} = w$$1.5 \text{lb} = w$$w = 1.5 \text{lb}$The weight of the item Bailey shipped was $\textcolor{red}{1.5 \text{lb}}\$