Question 39835: Maria, Mandy, and Crichton are on a dinosaur dig in Mexico. Each day they dig for fossils, and then check in with Leilani, who is the resident paleontologist, at the end of the day. Leilani helps the group to separate the fossils, those for the museum adn those they can keep. At the end of the first day 2/5 of the total goes to the museum. On the second day they find 6 new fossils and then 3/8 of the total goes to the museum. On the third day they find 13 new fossils adn that night the museum keeps 2/7 of the total. On the fourth day they add 7 and 4/9 goes to the museum. ON the fifth day they find 3 fossils and the museum keeps 5/6 of their total. They add 12 on the sixth day and the museum keeps 1/3 of their collection. At the end of their dig, Maria, Mandy and Crichton have 10 fossils to take home. HOw many new fossils did they collect for the museum?
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! I'm not told how many fossils they collect at the end of the first day.
All I'm told is that 2/5 of them go to the museum.
At he end of 6 days, I'm told they get to keep 10 fossils, so I
will try to count how many they have kept at the end of each day,
and keep a running total that will equal 10 when I'm done.
Let x equal the number of fossils they collect at the end of the 1st day
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They keep
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1) (3/5)x end of 1st day (2/5 went to museum)
2) ((3/5)x + 6)5/8 end of 2nd day (added 6 more and 3/8 went to museum)
3) (((3/5)x + 6)5/8 + 13)5/7 end of 3rd day (added 13, 2/7 to museum)
4) ((((3/5)x + 6)5/8 + 13)5/7 + 7)5/9 end of 4th day (added 7, 5/9 to museum)
5) (((((3/5)x + 6)5/8 + 13)5/7 + 7)5/9 + 3)1/6 5th day (add 3, 5/6 to museum)
6) ((((((3/5)x + 6)5/8 + 13)5/7 + 7)5/9 + 3)1/6 + 12)2/3 (add 12, 1/3 museum)
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This last expression is the number of fossils they keep after 6 days
and the problems states that it is 10.
((((((3/5)x + 6)5/8 + 13)5/7 + 7)5/9 + 3)1/6 + 12)2/3 = 10
multiply each side by 3/2
(((((3/5)x + 6)5/8 + 13)5/7 + 7)5/9 + 3)1/6 + 12 = 15
subtract 12 from both sides
(((((3/5)x + 6)5/8 + 13)5/7 + 7)5/9 + 3)1/6 = 3
multiply both sides by 6
((((3/5)x + 6)5/8 + 13)5/7 + 7)5/9 + 3 = 18
subtract 3 from both sides
((((3/5)x + 6)5/8 + 13)5/7 + 7)5/9 = 15
multiply both sides by 9/5
(((3/5)x + 6)5/8 + 13)5/7 + 7 = 27
subtract 7 from both sides
(((3/5)x + 6)5/8 + 13)5/7 = 20
multiply both sides by 7/5
((3/5)x + 6)5/8 + 13 = 28
subtract 13 from both sides
((3/5)x + 6)5/8 = 15
multiply both sides by 8/5
(3/5)x + 6 = 24
subtract 6 from both sides
(3/5)x = 18
multiply both sides by 5/3
x = 30
x was the amount of fossils collected on the 1st day
going back to 1)
-----------------------------------------
they keep-----------------------to museum
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1) 3/5(30) = 18 ----------------2/5(30) = 12
2) 5/8(18 +6) = 15 -------------3/8 (18 + 6) = 9
3) 5/7(15 + 13) = 20 -----------2/7(15 + 13) = 8
4) 5/9(20 + 7) = 15-------------4/9(20 + 7) = 12
5) 1/6(15 + 3) = 3--------------5/6(15 + 3) = 15
6) 2/3(12 + 3) = 10-------------1/3(12 + 3) = 5
They have 10 fossils after day 6 as they should.
To find how many fossils the museum has, add up the
"to museum" column
12 + 9 + 8 + 12 + 15 + 5 = 61 answer
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