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Real-Life Math -- Solution

Carat weight = diameter squared x depth x 0.0061

Carat weight = 5.7 x 5.7 x 3.66 x 0.0061
Carat weight = 0.725

0.725 x $2,978 = $2,159.05

That's a pretty good diamond. The person should be able to get $2,159.05 for it.

Jeweler Paul Wendt says an appraiser has to take into consideration the size of a stone and how it's cut. They often turn to books of tables to determine the carat weight, but you still have to do some adding and subtracting to come up with an accurate carat weight estimate.

"It's very traditional that you use books, but they're usually graduated by 0.2 [carat]," he says. But because every stone is different, and precise measurements aren't always easy to get, "sometimes you sit there and say, 'I get roughly 92 points.'

"The reality is, most of it is common sense. You can have a marquis-cut stone or a pear-shaped stone. But what if someone comes in with a heart-shaped stone?" says Wendt.

"Pearls are the easiest to appraise," he says.