SOLUTION: there were four times as many boys as girls at a party. After 105 boys left the party, there were twice as many girls as boys left. How many children were there altogether at first

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Question 867384: there were four times as many boys as girls at a party. After 105 boys left the party, there were twice as many girls as boys left. How many children were there altogether at first?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +b+ = the number of boys at first
Let +g+ = the number of girls at first
---------------------------------------------
(1) +b+=+4g+
(2) +g+=+2%2A%28+b+-+105+%29+
------------------------------
Substitute (1) into (2)
(2) +g+=+2%2A%28+4g+-+105+%29+
(2) +g+=+8g+-+210+
(2) +7g+=+210+
(2) +g+=+30+
and, since
(1) +b+=+4g+
(1) +b+=+4%2A30+
(1) +b+=+120+
----------------------
The number of children
at first = +b+%2B+g+
+b+%2B+g+=+120+%2B+30+
+b+%2B+g+=+150+
------------------------
check answer:
(2) +g+=+2%2A%28+b+-+105+%29+
(2) +30+=+2%2A%28+120+-+105+%29+
(2) +30+=+2%2A15+
(2) +30+=+30+
OK