SOLUTION: Hi 28% of the paperclips in a box are purple.the rest sre blue and black in the ratio 13:5.if there are 102 more blue than black, how many blue and black are altogether. Thank

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hi 28% of the paperclips in a box are purple.the rest sre blue and black in the ratio 13:5.if there are 102 more blue than black, how many blue and black are altogether. Thank      Log On

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Question 1098358: Hi
28% of the paperclips in a box are purple.the rest sre blue and black in the ratio 13:5.if there are 102 more blue than black, how many blue and black are altogether.
Thanks

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There is probably a typo somewhere,
because there seem to be some broken paperclips in that box.
To calculate the answer, I do not care about the purple paperclips.
All I care about is that the ratio of blue to black paperclips is 13:5.
That means that there are 13x blue paperclips and 5x black ones,
for some positive number x .
There are 13x%2B5x=18x black and blue paperclips altogether,
and 13x-5x=8x more blue paperclips than black paperclips.
It turns out that 8x=102 ,
so that x=102%2F8 and 18x=18%2A102%2F8=229.5 is the number v of blue and black paperclips altogether.

Now that I have a crazy answer,
I can have some fun calculating more crazy numbers.
x=102%2F8=12.75
The number of black paperclips is
5x=5%2A12.75=63.75 ;
the number of blue paperclips is
13x=13%2A12.75=165.75 ;
the number of purple paperclips is
229.5%2A%28%2228%25%22%2F%28%22100%25%22-%2228%25%22%29%29=229.5%2A28%2F72=89.25 ,
and the total number of paperclips in the box is
89.25%2B63.75%2B165.75=318.75 .