MATH F.1

two month ago, the total weight of lily and wendy was 150kg.they went to the gymnasium together to have fitness　training.now, the weight of lily drops by 2/5 anｄ the weight of wendy drops by 13/20 .if lily weight 5 kg less than wendy now , what were their respective weights two months ago?

let lily weight two months ago was X kg and wendy was Y kg.

X+Y=150 -----(1)
(1-13/20)Y - (1-2/5)X =5 -----(2)

from (1), X = 150-Y -----(3)

sub (3) into (2), (1-13/20)Y - (1-2/5)(150-Y) =5
7Y/20 - 3(150-Y)/5 = 5
7Y/20 - 12(150-Y)/20 =5
7Y - 1800 + 12Y = 100
19Y = 1900
Y = 100

sub Y=100 into (3), X = 150-100
X = 50

therefore lily weight two months ago was 50 kg and wendy was 100 kg.