SOLUTION: A concert was attended by 449 people and total sales were $4748. Adult tickets $12 and Children tickets $7. How many of each ticket bought?

Click here to see ALL problems on Miscellaneous Word Problems

Question 831673: A concert was attended by 449 people and total sales were $4748. Adult tickets $12 and Children tickets $7. How many of each ticket bought?
Found 2 solutions by stanbon, hovuquocan1997:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A concert was attended by 449 people and total sales were $4748. Adult tickets $12 and Children tickets $7. How many of each ticket bought?
-------
Quantity: a + c = 449
Value: 12a +7c = 4748
---------------------------
Modify for elimination:
12a + 12c = 12*449
12a + 7c = 4748
---------------------
Subtract and solve for "c":
5c = 640
c = 128 (# of children's tickets sold)
------
a + c = 449
a + 128 = 449
a = 321 (# of adult tickets sold)
--------------------
Cheers,
Stan H.
====================

Answer by hovuquocan1997(83) (Show Source):
You can put this solution on YOUR website!
Let the number of adults be x and the number of children be y
We have the total number of both is 449 people, so we have the first equation:
x + y = 449
Then we have the total cost of adult is 12x ($12 each ticket times the number of adults) and the total cost of children is 7y ($7 each ticket times the number of children) and the total cost of both is $4748 (given). So we have the second equation:
12x + 7y = 4748
Now as we have 2 equations, we can form a system of equation and solve for x and y

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve:
We'll use substitution. After moving 1*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: So, we know that y=128. Since , x=321.

Answer: .

You get x = 321 and y = 128
That means the number of adults are 321 and the number of children are 128
That means there are 321 adult tickets bought and 128 children tickets bought
TA-DAH
:D