SOLUTION: Some boys shared 455 stamps among themselves.1/2 of them received 5 stamps each 1/8 of them received 6 stamps each and the rest received 3 stamps each. How many boys are they altog

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Some boys shared 455 stamps among themselves.1/2 of them received 5 stamps each 1/8 of them received 6 stamps each and the rest received 3 stamps each. How many boys are they altog      Log On


   

Question 959348: Some boys shared 455 stamps among themselves.1/2 of them received 5 stamps each 1/8 of them received 6 stamps each and the rest received 3 stamps each. How many boys are they altogether?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the total number of boys
+455+ = the number of stamps
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1/2 of them received 5 stamps each
+%28+n%2F2+%29%2A5+ is that number of stamps
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1/8 of them received 6 stamps each
+%28n%2F8%29%2A6+ is that number of stamps
-----------------------------------
The rest received 3 stamps each
+%28+n+-+n%2F2+-+n%2F8+%29%2A3+ is that number of stamps
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Now I can say:
+%28n%2F2%29%2A5+%2B+%28n%2F8%29%2A6+%2B+%28+n+-+n%2F2+-+n%2F8+%29%2A3+=+455+
+%28+5%2F2+%29%2An+%2B+%28+3%2F4+%29%2An+%2B+%28+9%2F8+%29%2An+=+455+
Multiply both sides by +24+
+12%2A5%2An+%2B+3%2A6%2An+%2B+3%2A9%2An+=+10920+
+60n+%2B+18n+%2B+27n+=+10920+
+105n+=+10920+
+n+=+104+
There are 104 boys altogether
check:
1/2 of them received 5 stamps each
+%28+n%2F2%29%2A5+=+52%2A5+
+52%2A5+=+260+
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1/8 of them received 6 stamps each
+%28+n%2F8+%29%2A6+=+%28+104%2F8+%29%2A6+
+%28+104%2F4+%29%2A3+=+26%2A3+
+26%2A3+=+78+
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The rest received 3 stamps each
+%28+3%2F8+%29%2An%2A3+=+%28+3%2F8+%29%2A104%2A3+
+%28+9%2F8+%29%2A104+=+117+
------------------------
+260+%2B+78+%2B+117+=+455+
+455+=+455+
OK