SOLUTION: Rs 400 be divided among 6 men,12 women and 17 boys so that 2 men receive as much as 5 boys and 2 women as much as 3 boys.how much will one man ,one woman and one boy get in total?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Rs 400 be divided among 6 men,12 women and 17 boys so that 2 men receive as much as 5 boys and 2 women as much as 3 boys.how much will one man ,one woman and one boy get in total?       Log On


   

Question 1015115: Rs 400 be divided among 6 men,12 women and 17 boys so that 2 men receive as much as 5 boys and 2 women as much as 3 boys.how much will one man ,one woman and one boy get in total?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = share for 1 man
Let +b+ = share for 1 woman
Let +c+ = share for 1 boy
----------------------------
(1) +6a+%2B+12b+%2B+17c+=+400+
(2) +2a+=+5c+
(3) +2b+=+3c+
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(2) +a+=+%285%2F2%29%2Ac+
(3) +b+=+%283%2F2%29%2Ac+
--------------------
Substitute (2) and (3) into (1)
(1) +6a+%2B+12b+%2B+17c+=+400+
(1) +6%2A%285%2F2%29%2Ac+%2B+12%2A%283%2F2%29%2Ac+%2B+17c+=+400+
(1) +15c+%2B+18c+%2B+17c+=+400+
(1) +50c+=+400+
(1) +c+=+8+
and
(2) +a+=+%285%2F2%29%2Ac+
(2) +a+=+%285%2F2%29%2A8+
(2) +a+=+20+
and
(3) +b+=+%283%2F2%29%2Ac+
(3) +b+=+%283%2F2%29%2A8+
(3) +b+=+12+
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1 man, 1 woman, and 1 boy will get:
+20+%2B+12+%2B+8+=+40+
----------------------
check:
(1) +6a+%2B+12b+%2B+17c+=+400+
(1) +6%2A20+%2B+12%2A12+%2B+17%2A8+=+400+
(1) +120+%2B+144+%2B+136+=+400+
(1) +400+=+400+
OK