Question 1202861
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Jon had red and blue pencils. He put them into Boxes X and Y. 
Box X had 2 times as many pencils as Box Y. 
All the pencils in Box X were red. 
In Box Y, the ratio of the number of red pencils to the number of blue pencils was 8:1.
(a) What fraction of the total number of pencils in both boxes were blue? 
Give your answer in the simplest form.
(b) There were 90 more red pencils in Box X than in Box Y. 
How many blue pencils were there altogether?
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Let "b" be the number of blue pencils in box Y.

Then the number of red pencils in box Y is 8b,
     the number of all pencils in box Y is b + 8b = 9b,
and  the number of red pencils in box X is 2*(9b) = 18b.


Now the answer to question (a) is  {{{b/(18b + 9b)}}} = {{{b/(27b)}}} = {{{1/27}}}.



For (b), we have 8b red pencils in box Y and 18b red pencils in box X.

From the problem, we have this equation

    18b - 8b = 90

      10b    = 90

        b    = 90/10 = 9.


So, there are 9 blue pencils in box Y, which means that there are 9 blue pencils in both boxes, altogether.
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Solved.