SOLUTION: 80% of the people at a concert were adults. 75% of the children at a concert were boys. There were 36 more boys than girls. a. How many boys were there at a concert? b. Some bo

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Question 1140590: 80% of the people at a concert were adults. 75% of the children at a concert were boys. There were 36 more boys than girls.
a. How many boys were there at a concert?
b. Some boys left halfway through the concert after which 10% of the remaining people at the concert were boys. How many boys left the concert halfway?
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.

            I will answer question (a) only. 


Let x be the number of girls.


Then the number of boys is 3x, from the condition.


You are given that   3x - x = 36,   or   2x = 36;  hence,  x = 36/2 = 18  is the number of girls.


Then the number of boys is  3x = 3*18 = 54.    ANSWER



Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = total number at the concert
+.2%2A.75x+=+.15x+ is the number of boys
+.2%2A.25x+=+.05x+ is the number of girls
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+.15x+=+.05x+%2B+36+
+.1x+=+36+
+x+=+360+
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(a)
+.15%2A360+=+54+ is the number of boys at concert
(b)
Let +n+ = number of boys who left concert
+.1%2A%28+x+-+n+%29+=+54+-+n+
+.1%2A%28+360+-+n+%29+=+54+-+n+
+36+-+.1n+=+54+-+n+
+.9n+=+54+-+36+
+.9n+=+18+
+n+=+20+
20 boys left the concert
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check:
+360+-+20+=+340+ people remain after 20 boys left
+.1%2A340+=+34+ boys remain after 20 boys left
+34+%2B+20+=+54+ is number of boys starting out
OK