Question 1008195
m = # of men
w = # of women
c = # of children
t = total number of passengers on the train


45% of the passengers are women, so
w = 0.45t


30% of the passengers are men, so
m = 0.30t


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"there are 120 more women than men on the train" means
w = m+120


Now plug in m = 0.30t and w = 0.45t


w = m+120
w = 0.30t+120
0.45t = 0.30t+120


and isolate t


0.45t = 0.30t+120
0.45t - 0.30t = 120
0.15t = 120
t = 120/0.15
t = 800


There are 800 people on the train


"25% are children", so


c = 25% of 800 = 0.25*800 = 200


There are 200 children on the train