A cash for gold website operates by getting customers to mai

A cash for gold website operates by getting customers to mail gold to the sites processing facility. There, the gold is weighed and checked for purity. The weight and purity levels are used to compute the market value of the gold. The website then sends customer a check for the gold\'s value minus a 15% fee. What was the weight (in grams) of Cynthia\'s necklace? The market values for gold of different purity levels (in karats) are given in the table below. Cynthia sends a necklace made of 18-kurat gold to the website. She receives a check for $I37.70 in return. Cynthia also has a collection of gold bracelets; each weigh 1.1 grams However, she does not know the purity of the gold in the bracelets. If she sends 7 of the bracelets in to the website, what is the difference I rounded to the nearest dollar) between the largest amount she could get in return and the smallest amount?

Solution

Let the weight of Cynthia’s necklace be x grams. Then, the value of the necklace is $ 36x. Since the “cash for gold” website sends a cheque after deducting 15 % fee, hence 36x * 85 % = 137 .70 or, 36x*85/100 = 137.70 or, 3060x = 13770 so that x = 13770/3060 = 4.5 grams. Thus, the weight of Cynthia’s necklace is 4.5 grams.

The total weight of Cynthia’s 7 gold bracelets is 7 *1.1 = 7.7 grams. Further, 85 % of 7.7 grams is 6.545 grams. If the purity of the gold bracelets is 24 k, Cynthia will get $ 41* 6.545 = $ 268.345. Further, if the purity of the gold bracelets is 10 k, Cynthia will get $ 17 *6.545 = $ 111.265. Thus, the difference between the largest and the smallest amounts that Cynthia could get is $ 268.345 - $ 111.265 = $ 157.08 or $ 157 ( on rounding off to the nearest Dollar).