SOLUTION: There are 270 men, women and children on a train. The ratio of men to women is 4:5 The ratio of women to children is 10:9 How many men are on the train ?

Question 1130527: There are 270 men, women and children on a train.
The ratio of men to women is 4:5
The ratio of women to children is 10:9
How many men are on the train ?
Found 3 solutions by josmiceli, Boreal, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = number of men
Let = number of women
Let = number of children
---------------------------------------
(1)
(2)
(3)
--------------------------------
(2)
(3)
Substituting:
(1)
Multiply both sides by
(1)
(1)
(1)
and
(2)
(2)
and
(3)
(3)
----------------------------
80 men are on the train
----------------------------
check:

OK
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
4 men to 5 women
40 men to 50 women, and since it is 10:9 women to children, that would be 45 children, since 50:45 is 10:9
Therefore, 40:50:45, which adds to 135. Twice that would be 270
That is 80 men, 100 women, and 90 children
80. ANSWER
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

The ratio of children to women is . The ratio of men to women is = . In other words, for each 10 women, there are 9 men and 8 children. So, we can group all the people in the train in groups consisted of 10 women, 9 men and 8 children each. Every such group consists of 10+9+8 = 27 persons, so the number of groups is = 10. Answer. There are 10*10= 100 women, 9*10 = 90 men and 8*10 = 80 children in the train. CHECK. 100 + 90 + 80 = 270. ! Correct !

Solved (mentally).

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