SOLUTION: concert tickets cost $24 an adult, $15 a child, and $12 a senior, If they made $5670 dollars, and 5 times as many adults attended as seniors, and 2 times as many children attended

Algebra ->  Matrices-and-determiminant -> SOLUTION: concert tickets cost $24 an adult, $15 a child, and $12 a senior, If they made $5670 dollars, and 5 times as many adults attended as seniors, and 2 times as many children attended       Log On


   



Question 393885: concert tickets cost $24 an adult, $15 a child, and $12 a senior, If they made $5670 dollars, and 5 times as many adults attended as seniors, and 2 times as many children attended then seniors, how could i set up a system of equations ,and find how much of each ticket was sold?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = number of senior tickets sold
Let b = number of child tickets sold
Let c = number of adult tickets sold
------------
given:
12a+%2B+15b+%2B+24c+=+5670
c+=+5a
b+=+2a
Now by substitution:
12a+%2B+15%2A%282a%29+%2B+24%2A%285a%29+=+5670
12a+%2B+30a+%2B+120a++=+5670
162a+=+5670
a+=+35
and, since
c+=+5a
c+=+175
and, also
b+=+2a
b+=+70
35 senior, 70 child, and 175 adult tickets were sold
Check answer by plugging back into
12a+%2B+15b+%2B+24c+=+5670