SOLUTION: The ratio of the number of the men to the number of women at a football match was 4:3.The ratio of the number of women to the ratio of children was 5:2 .There were 56 more men than

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of the number of the men to the number of women at a football match was 4:3.The ratio of the number of women to the ratio of children was 5:2 .There were 56 more men than      Log On


   

Question 1079457: The ratio of the number of the men to the number of women at a football match was 4:3.The ratio of the number of women to the ratio of children was 5:2 .There were 56 more men than children .How many people were at the football match
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the number of men
Let +b+ = the nuber of women
Let +c+ = the number of children
----------------------------------
(1) +a%2Fb+=+4%2F3+
(2) +b%2Fc+=+5%2F2+
(3) +a+=+c+%2B+56+
---------------------
Multiply (1) times (2)
+%28+a%2Fb+%29%2A%28+b%2Fc+%29+=+%284%2F3%29%2A%285%2F2%29+
+a%2Fc+=+10%2F3+
+c+=+%283%2F10%29%2Aa+
Plug this result into (3)
+a+=+%283%2F10%29%2Aa+%2B+56+
+%287%2F10%29%2Aa+=+56+
+a+=+%2810%2F7%29%2A56+
+a+=+80+
and
(3) +80+=+c+%2B+56+
(3) +c+=+24+
and
(1) +a%2Fb+=+4%2F3+
(1) +b+=+%283%2F4%29%2Aa+
(1) +b+=+%283%2F4%29%2A80+
(1) +b+=+60+
----------------------
+a+%2B+b+%2B+c+=+80+%2B+60+%2B+24++
+a+%2B+b+%2B+c+=+164+
There were 164 people at the game
-----------------------------------
check:
(1) +a%2Fb+=+4%2F3+
(1) +80%2F60+=+4%2F3+
(1) +4%2F3+=+4%2F3+
OK
You can check (2) and (3)