Question

Elaine bought 11 feet 8 inches of fancy ribbon for$392. The spool was stained and some length ofthe ribbon was soiled and not usable. She quicklysold the remaining ribbon to George at a per-inchprice of 3/7 higher than she paid for it. Altogether,she made a profit of $28. What percentage of theribbon was soiled?

Answer 1

`\begin{gathered} \text{Elaine bought the ribbon for 392, and the total spool was 11 f}et\text{ 8 inches} \\ \text{That means she bought at the rate of} \\ 11ft8in=140inches \\ 140in=392\text{ dollars} \\ 1in=(392)/(140) \\ 1in=2.8\text{ dollars} \\ When\text{ selling to George, she now sold at a rate which is 3/7 higher than she bought it.} \\ \text{This means } \\ \text{Selling price=2.8+(2.8 x }(3)/(7)) \\ \text{Selling price=2.8+1.2} \\ \text{Selling price=4 dollars per inch} \\ \text{If she made a profit of \$28, then it means } \\ \text{Profit}=\text{Sellingprice}-\text{Costprice} \\ 28=\text{Sellingprice}-392 \\ \text{Selling Price=28+392} \\ \text{Selling price=420} \\ \text{If Elaine sold the ribbon for \$420 at the rate of \$4 per inch, then that means} \\ \text{Ribbons sold=}(420)/(4) \\ \text{Ribbons sold=105 inches} \\ Hence,\text{ the percentage of ribbons soiled would be} \\ \text{Soiled}=\text{Bought}-\text{Sold} \\ \text{Soiled}=140in-105in \\ \text{Soiled}=35in \\ \text{percentage soiled therefore would be derived as;} \\ Percentage\text{Soiled}=(35)/(140)*100 \\ Percentage\text{Soiled}=25 \end{gathered}`

The percentage of the ribbon that was soiled was therefore 25%