Question

Mickey and Minnie shared a box of matches. If Mickey was given 10 fewer matches, Minnie would have 5 times as many matches as Mickey.
If Mickey was given 10 more matches, he would have 1/2 as many matches as Minnie.
What percentage of matches did Mickey receive?

Answer 1

let Minnie has = x matches
Mickey has = y matches
Now,
x = 5 (y - 10)
=> x = 5y - 50
=> x - 5y = - 50 — (1)
Now,
y + 10 = 1/2x
=> 2y + 20 = x => x - 2y = 20 — (2)
from (1) & (2)
-3y = -70 => y = 70/3
=> x = 2 * 70/3 + 20 = 210/3
Mickey = 70/3/210/3 * 100 = 25.92%