Will, Xavier and George had a total of 670 pens. The ratio of the number of pens Xavier had to the number of pens George had was 4:5. After Will and Xavier each gave away half of their pens, the 3 children had 395 pens left. How many pens did Xavier and George have at first?

Answer 1

w + x + g = 670 (1)
x : g = 4:5 (2)
1/2 (w + x) = 670 - 395 (3)

(2) => g = 5/4x (4)
(3) => w = 550 - x (5)
Put (4) and (5) into (1)
=> 550 - x + x + 5/4x = 670
5/4x = 120
x = 96

g = 5/4 * 96 = 120
w = 550 - 96 = 454
x = 96
g = 120
w = 454

Answer 2

let the number of pens each had to start with be
Will: w
Xavier: 4x
George: 5x
Then we are told that
w + 4x + 5x = 670
w/2 + 2x + 5x = 395
rewrite that as
w + 9x = 670
w + 14x = 790
now subtract to get
5w = 120
w = 24
So
Xavier+George = 96+120 = 216