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The graph shows the price ranges for five weights of diamond rings at a jewelry store. The jewelry store had a diamond ring listed at $11,499. What is the carat weight of the diamond ring? Explain your reasoning. (See Example 5 and Example 6.)
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The price range for a 0.30-carat diamond ring is
The price range for a 0.50-carat diamond ring is
The price range for a 1.00-carat diamond ring is
The price range for a 2.00-carat diamond ring is
Because $11,499 falls in the range $6892 through $16,092, the carat weight of the diamond ring is 2.00 carats.
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When posting a comment, you agree to our Terms of Use.Showing 1 commentsRon Larson (author)1 decade ago |This type of graph is called a waterfall graph. The numbers on the graph (like $9200) show the increase in price from the previous price.0 1 -
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The graph shows the price ranges for five weights of diamond rings at a jewelry store. What is the price range of a 1.00-carat diamond ring? (See Example 5 and Example 6.)
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The graph shows the price ranges for five weights of diamond rings at a jewelry store. How much more does a 2.00-carat diamond ring cost than a 1.00-carat diamond ring? (See Example 5 and Example 6.)
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The lower-end price for a 1.00-carat diamond ring is
The upper-end price for a 1.00-carat diamond ring is
The upper-end price for a 2.00-carat diamond ring is
So, at the one extreme, a 2.00-carat diamond ring could cost
more than a 1.00-carat diamond ring. Or, at the other extreme, the two rings could be about equal in price.
Comparing jewelry prices is difficult. There are several categories of jewelry stores. Stores like Kay, Jared, and Zales tend to be located in middle-class malls and cater to a typical middle-class consumer. Discount jewelers cater to bargin shoppers. Designer stores like Cartier, Tiffany, and Bvlgari cater to wealthy customers.
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The graph shows the price ranges for five weights of diamond rings at a jewelry store. Reword the statement so it uses a percent that is greater than 200%. (See Example 5 and Example 6.)
A 0.50-carat diamond ring costs $2026, which is about 108.7% more than the cost of a 0.30-carat diamond ring.
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Is it true that a 0.50-carat diamond is more than 60% larger than a 0.30-carat diamond? Explain your reasoning. (See Example 5 and Example 6.)
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A 0.50-carat diamond weighs 0.20 carat more than a 0.30-carat diamond.
So, it is true that a 0.50-carat diamond is more than 60% heavier than a 0.30-carat diamond. On the other hand, the word "larger" can be misleading. It is not true that the 0.50-carat diamond has a diameter that is more that 60% greater. As diamonds increase in carat weight, their diameter roughly increases as the cube root of the weight (see the following comparisons). When comparing widths (what you see), a 0.50-carat diamond has a diameter (5.2 mm) that is only 21% greater than the diameter (4.3 mm) of a 0.30-carat diamond.
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The graph shows the price ranges for five weights of diamond rings at a jewelry store. Use percent to describe the change in maximum price. (See Example 5 and Example 6.)
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from a 0.50-carat diamond ring to a 1.00-carat diamond ring
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from a 1.00-carat diamond ring to a 2.00-carat diamond ring
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from a 2.00-carat diamond ring to a 3.00-carat diamond ring
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Use percent to describe the change in carat weight. (See Example 5 and Example 6.)
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from a 0.50-carat diamond ring to a 1.00-carat diamond ring
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from a 1.00-carat diamond ring to a 2.00-carat diamond ring
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from a 2.00-carat diamond ring to a 3.00-carat diamond ring
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A 1.00-carat diamond weighs 0.50 carat more than a 0.50-carat diamond.
So, to change from a 0.50-carat diamond to a 1.00-carat diamond is an increase of 100%.
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A 2.00-carat diamond weighs 1.00 carat more than a 1.00-carat diamond.
So, to change from a 1.00-carat diamond to a 2.00-carat diamond is an increase of 100%.
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A 3.00-carat diamond weighs 1.00 carat more than a 2.00-carat diamond.
So, to change from a 2.00-carat diamond to a 3.00-carat diamond is an increase of 50%.
Although diamonds are not particularly rare, extracting diamonds is laborious. Mines move many tons of dirt per carat of diamond found. Large gem-quality diamonds are relatively rare. Only about 1 in 1 million diamonds are quality 1-carat stones, only 1 in 5 million are 2-carat, and 1 in 15 million are 3-carat.
Most of the natural diamonds mined and sold are controlled by a company called De Beers. To maintain the high prices of diamonds, De Beers creates an artificial scarcity by stockpiling diamonds and selling them in small amounts.
In 2004, astronomer Travis Metcalfe of the Harvard-Smithsonian Center for Astrophysics and colleagues discovered a diamond star that is 10 billion trillion trillion carats! "The cosmic diamond is a chunk of crystallised carbon, 4,000 km across, some 50 light-years from the Earth in the constellation Centaurus. It's the compressed heart of an old star that was once bright like our Sun but has since faded and shrunk." (source: BBC News)
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The graph shows the price ranges for five weights of diamond rings at a jewelry store. Describe the relationship between carat weight and price of a diamond ring. (See Example 5 and Example 6.)
These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.
When posting a comment, you agree to our Terms of Use.