SOLUTION: At a football match,there were 250 more men than women.The number of children was twice the number of women. If the number of men was twice the number of children and women togethe

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: At a football match,there were 250 more men than women.The number of children was twice the number of women. If the number of men was twice the number of children and women togethe      Log On


   

Question 1007524: At a football match,there were 250 more men than women.The number of children was twice the number of women. If the number of men was twice the number of children and women together,, how many people watched the match ??
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = number opf men
Let +w+ = number of women
Let +c+ = number of children
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given:
(1) +m+=+w+%2B+250+
(2) +c+=+2w+
(3) +m+=+2%2A%28+c+%2B+w+%29+
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There are 3 equations and 3 unknowns,
so it's solvable
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Substitute (2) into (3)
(3) +m+=+2%2A%28+2w+%2B+w+%29+
(3) +m+=+2%2A%28+3w+%29+
(3) +m+=+6w+
Substitute (3) into (1)
(1) +6w+=+w+%2B+250+
(1) +5w+=+250+
(1) +w+=+50+
and
(3) +m+=+6w+
(3) +m+=+6%2A50+
(3) +m+=+300+
and
(2) +c+=+2w+
(2) +c+=+2%2A50+
(2) +c+=+100+
There were 100 children, 50 women, and 300 men, so
+100+%2B+50+%2B+300+=+450+ people watched the match
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check:
(3) +m+=+2%2A%28+c+%2B+w+%29+
(3) +300+=+2%2A%28+100+%2B+50+%29+
(3) +300+=+2%2A150+
(3) +300+=+300+
OK -you can check (1) and (2)