Question

Brian spent 1/3 of his money on 5 pens and 11 erasers. The cost of each pen is 3 times the cost of each eraser. He bought some more pens with 3/4 of his money. How many pens did Brian buy altogether?

Answer 1

Since 1/3 + 3/4 > 1, I am assuming that by "3/4 of his money" you mean 3/4 of the 2/3 he had left, or 1/2 of his total money.
the cost p = 3e
5p+11e = x/3
so 5p + 11p/3 = x/3
26p/3 = x/3
now, 1/2 = 3/2 * 1/3, so
3/2 * 26p/3 = 13p
He bought 13+5 = 18 pens

Answer 2

Cost of 5 pens = 5u
Cost of 11 pens = 11v
5u + 11v = x/3
Since, u = 3v
-> 15v + 11v = x/3
-> 26v = x/3
-> v = x/3*26 = x/78 -> 78v
-> cost of an eraser = x/78
-> cost of a pen = 3 * x/78 = x/26

He bought some more pens with 3/4 of his money.
After spending x/3 money on 5 pens and 11 erasers, Brian left with x - x/3 = 2x/3
money. : 3/4 of 2x/3 = 3/4 * 2x/3 = x/2

He spent x/2 money on some more pens.

Since, x = 78v, v = u/3 where u
is cost of a pen

-> x = 78 * u/3 = 26u
: x/2 = 26u/2 = 13u

Since u is cost of a pen,
13u is cost of 13 pens
-> Extra pens = 13
: Total number of pens
= Extra number of pens + 5 pens
= 13 + 5
= 18
-> Brian buy 18 pens altogether.