Wesley bought some blue pens and gave half of them to Joshua. Joshua bought some
black pens and gave half of them to Wesley. Wesley used 3 black pens and Joshua used
6 blue pens. After that, the number of black pens Wesley had was 1/6 of the number of
blue pens he had while the number of black pens Joshua had was 1/4 of the number of
blue pens he had.
(a) How many blue pens did Wesley buy?
(b) How many black pens did Joshua buy?
THIS IS AN ENGLISH QUESTION MY BRAIN IS MELTING BY LOOKING AT IT
10 years later...
Answer: Wesley bought 108 blue pens and Joshua bought 24 black pens.
Distribution of the pens after using some of them:
Wesley: Half the blue pens, half the black pens - 3
Joshua: Half the blue pens - 6, half the black pens
Let x be half the number of blue pens. Let y be half the number of black pens (they both got half):
x = 6(y - 3)
x - 6 = 4y
I'll use substitution to solve this:
6(y - 3) - 6 = 4y
6y - 18 - 6 = 4y
2y = 24
y = 12
Putting that back into one of the equations and solving it gives x = 54.
BUT I used the half number as my variables, so I'll double the numbers at this point to get (x, y) = (108, 24) or in the question terms, Wesley bought 108 blue pens and Joshua bought 24 black pens.