+38 Wayne has 7/13 of the number of stamps that Monica has. After Peter gave an equal number of stamps to Wayne and Monica, Wayne has 9/10 of the number of stamps that Monica has. if the number of stamps Peter gave to Wayne is between 500 and 550, what is the number of stamps that Peter gave to Monica?
M has x
W has 7/13x
P give w y stamps and M y stamps.
So after that, M has x + y & w has 7/13x + y
and 7/13x + y = (x + y) 9/10, 500 < y < 550
7/13x + y = 9/10x + 9/10y
1/10y = 47/130x
y = 47/13x
The important is x, y lol are positive integers.
coz 500 < y < 550 => 500 < 47/13x < 550
138.30 < x < 152.13
By analyzing, x should be removed by 13
13 * 10 = 130; 13 * 11 = 143; 13 * 12 = 156. Only 138 < 143 < 152
So x = 143 => y = 517
All in all P give M 517 stamps.
