Counting Shipwrecked Treasure - Ms. Krevitsky (best ebook pdf reader android .TXT) 📗

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Barry Ed Treasure is fascinated by treasures in sunken ships.  He keeps a journal about each of the ships he visits and the treasure he recover  However, as soon as he brings the treasure up, he gives it to his assistant, Zuzzle, to catalog.  Unfortunately, his assistant is often very forgetful.  He usually forgets to record how many of each kind of treasure were recovered.  Can you help Zuzzle discover how many of each type of treasure were recovered from the ships?

 

Photo by Tom Praison on Flickr

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Barry Treasure’s Journal

May 2, 2013

            Today was quite a day.  I have been searching for treasure off the coast of southern Argentina.  After weeks of searching, today I found a sunken ship.  The ship appears to have been called The Marana, and it looks like it has been underwater for many years.  I did locate a great treasure in the shipwreck.  I spent about 10 hours recovering the loot today, and my assistant Zuzzle stayed in the boat helping me.  I remember bringing up six loads of treasure with four items in each load.  It was quite a busy day for me, and I am going to get some rest.

Photo by Liam Quinn on Flickr

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Barry Treasure’s Journal

May 7, 2013

            Zuzzle told me today that he sold all of the treasure that I recovered from this shipwreck to a pawn shop.  He gave me the $16,000 he collected from selling all of the items I recovered.  I had some gold coins and some jewels, but he forgot to record how many of each type he sold.  I know that the shop buys antique shipwrecked coins for $800 each and jewels for $600 each.  I hope that he will be able to figure out how many of each type of treasure I had recovered.

Photo by Peter Richardson       Photo by Jeremy Schultz 

on Flickr                               on Flickr

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Can you help Zuzzle?

Barry Treasure asked Zuzzle to try to identify how many of each type of treasure was recovered from the shipwreck.  Zuzzle started by listing all of the information he knows about the treasure.

Barry Treasure recovered four items on each of his six trips up from the ship. In total he collected 4 x 6 = 24 items. All of the treasure was worth $16,000. Gold coins sell for $800 each. Jewels sell for $600 each. 5

 

Zuzzle realizes that he could try guessing different combinations of gold coins and jewels, but he doesn’t think Barry Treasure will be happy with the amount of time required for that method.  He realizes that he could use a variable to represent the number of gold coins and the number of jewels.  He decides to call the number of gold coins “g” and the number of jewels “j.”  Do you think you could write equations to model the information that Zuzzle knows about the treasure?  Try it out before you turn the page to see what Zuzzle did.

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Zuzzle first started out by looking at the information he knew about the money he collected from selling the treasure.  He remembered that each jewel sold for $600 and each gold coin sold for $800, and he collected a total of $16,000 from the shop.  He wrote out the following equation:

600j + 800g = 16000

Then, he realized that he would need another equation in order to find the number of jewels and gold coins because his equation had two variables, j and g.  So, he looked at the number of items that he sold to the shop.  He knew that he only sold jewels and gold coins, and he sold a total of 24 items.  He wrote out the following equation to model the information:

j + g = 24

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Zuzzle now has two equations that model the information about the treasure.

600j + 800g = 16000

j + g = 24

He thought that he could represent the number of jewels he sold as the total number of objects minus the number of gold coins.

j = 24 – g

How could Zuzzle use this information to find out the number of each kind of treasure?  See if you can figure it out before you turn the page to find out what Zuzzle did.

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He thought that he could use the equation about the money he was given to find the number of each kind of treasure.  He substituted 24 – g for j, the number of jewels in the money equation.

600(24 – g) +800g = 16000

After distributing the 600, he wrote the equation 14400 – 600g + 800g = 16000 and by combining the like terms he obtained 14400 + 200g = 16000.  The 14,000 represents the total amount of money he would have been given if all 24 items had been jewels.  The 200 in front of the g represents the difference in money earned between a jewel ($600) and a gold coin ($800).  While solving for g, he obtained the equation 200g = 1600 by subtracting 14400 from both sides of the equation.  Then, after dividing both sides by 200, he obtained the equation g = 8.  He knew that he must have sold 8 gold coins to the shop.

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After he knew how many gold coins he sold, he could easily discover the number of jewels he sold.  In total he sold 24 items and he knows that 8 of them were jewels.  Since 24 – 8 = 16, he must have sold 16 jewels.  At last, he can tell Barry Treasure how many of each kind of treasure was recovered from the ship.  Barry recovered 16 jewels and 8 gold coins.