SOLUTION: At a thearer, 400 tickets were sold. The ticket prices were $8, $10, and $12. The total income from ticket sales was $3700. How many tickets of each type were sold if the combined

Question 574467: At a thearer, 400 tickets were sold. The ticket prices were $8, $10, and $12. The total income from ticket sales was $3700. How many tickets of each type were sold if the combined number of $8 and $10 tickets sold was seven times the number of $12 tickets sold.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = number of $8 tickets
Let = number of $10 tickets
Let = number of $12 tickets
given:
(1)
(2)
(3)
--------------
This is 3 equations and 3 unknowns, so
it should be solvable
Substitute (3) into (1)
(1)
(1)
(1)
Plug this value into (2)
(2)
(2)
(2)
(2)
and
(1)
(1)
(1)
Multiply both sides of (1) by
(1)
Subtract (1) from (2)
(2)
(1)

and, since
(3)
(3)
(3)
(3)
There are 200 $8 tickets
There are 150 $10 tickets
There are 50 $12 tickets
check:
(2)
(2)
(2)
OK
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