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 ?

Algebra ->  Percentage-and-ratio-word-problems -> 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 ?      Log On


   

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) About Me  (Show Source):
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Let +a+ = number of men
Let +b+ = number of women
Let +c+ = number of children
---------------------------------------
(1) +a+%2B+b+%2B+c+=+270+
(2) +4%2F5+=+a%2Fb+
(3) +10%2F9+=+b%2Fc+
--------------------------------
(2) +a+=+%284%2F5%29%2Ab+
(3) +c+=+%289%2F10%29%2Ab+
Substituting:
(1) +%284%2F5%29%2Ab+%2B+b+%2B+%289%2F10%29%2Ab+=+270+
Multiply both sides by +10+
(1) +8b+%2B+10b+%2B+9b+=+2700+
(1) +27b+=+2700+
(1) +b+=+100+
and
(2) +a+=+%284%2F5%29%2A100+
(2) +a+=+80+
and
(3) +c+=+%289%2F10%29%2A100+
(3) +c+=+90+
----------------------------
80 men are on the train
----------------------------
check:
+80+%2B+100+%2B+90+=+270+
+270+=+270+
OK

Answer by Boreal(15235) About Me  (Show Source):
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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(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.
The ratio of children to women is  9%2F10.


The ratio of men to women is  4%2F5 = 8%2F10.


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  270%2F27 = 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).