SOLUTION: Linda was selling tickets for the school play. she sold 10 more adult tickets than children tickets and she sold as many senior tickets as children tickets, Adult tickets were sold

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Question 524702: Linda was selling tickets for the school play. she sold 10 more adult tickets than children tickets and she sold as many senior tickets as children tickets, Adult tickets were sold for $5, children tickets were $2 and senior tickets were for $3. Linda made a total of $700. How many of each type of ticket Linda sold
Answer by josmiceli(9661) About Me  (Show Source):
You can put this solution on YOUR website!
Let c = number of children's tickets sold
Let a = number of adult tickets sold
Let s = number of senior tickets sold
given:
(1) +a++=+c+%2B+10+
(2) +s+=+c+
(3) +2c+%2B+5a+%2B+3s+=+700+
-----------------------
Substitute (1) and (2) into (3)
(3) +2c+%2B+5%2A%28c%2B10%29+%2B+3c+=+700+
(3) +2c+%2B+5c+%2B+50+%2B+3c+=+700+
(3) +10c+=+650+
(3) +c+=+65+
and, since
(2) +s+=+c+
(2) +s+=+65+
also
(1) +a+=+c+%2B+10+
(1) +a+=+65+%2B+10+
(1) +a+=+75+
Linda sold
65 children's tickets
75 adult tickets
65 senior tickets
check:
(3) +2c+%2B+5a+%2B+3s+=+700+
(3) +2%2A65+%2B+5%2A75+%2B+3%2A65+=+700+
(3) +130+%2B+375+%2B+195+=+700+
(3) +700+=+700+
OK