100 marbles are placed in 3 bowls. How many marbles does the 3d bowl contain
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100 marbles are placed in 3 bowls. How many marbles does the 3d bowl contain

[From: ] [author: ] [Date: 13-03-05] [Hit: ]
-Begin by naming the marbles in the bowls with variables.so, there are 100 marbles,c=44-There are 100 marbles and 3 bowls.If there are 56 marbles in the first two bowls, then there are 100 - 56 = 44 marbles left over.......
The first and second bowls contain 56 marbles together . The second and 3d bowls contain 70 marbles together. How many marbles does the 3d bowl contain?
24, 30,36,44, or not enough info


Please help me! I am studying for a local math contest , I can't get my head around this type of question.

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Begin by naming the marbles in the bowls with variables.
marbles in 1st bowl= a
marbles in 2nd bowl= b
marbles in 3rd bowl= c

so, there are 100 marbles, which means a+b+c=100
a+b=56 therefore a=56-b
b+c=70 therefore c=70-b

Now let's replace a and c with their expressions
56-b+b+70-b=100
126-b=100
b=126-100
b=26

replace b with 26 in b+c=70
26+c=70
c=70-26
c=44

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There are 100 marbles and 3 bowls.

If there are 56 marbles in the first two bowls, then there are 100 - 56 = 44 marbles left over. Since there are only 3 bowls, and all the marbles are in a bowl, that means all 44 of the remaining marbles must be in that third one.

Done!

-
44
First bowl: 26 marbles
Second Bowl: 30 marbles
Third bowl: 44 marbles
1
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