+164 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?
+308 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.
Solution:
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.
