Tickets for a play at the community theater cost $12 for an adult and $8 for a child. If 150 tickets were sold and the total receipts were $1640, how many of each type of ticket were sold?
2007-01-21 12:58:46 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Let A denote the # of adult tickets sold.
150 - A = # of child tickets sold.
12A + 8(150 - A) = 1640
12A + 1200 - 8A = 1640
4A = 1640 - 1200
4A =440
A = 110 adult tickets sold.
150 - 110 = 40 children's tickets sold.
Check:
12(110) + 8(40) = 1320 + 320 = 1640.
2007-01-21 13:05:59 · answer #1 · answered by S. B. 6 · 0⤊ 0⤋
When doing all these kinds of problems, first identify variables for the things you are trying to find out. In this problem that is the number of child tickets and the number of adult tickets sold, so:
c= number of child tickets
a= number of adult tickets
Then you just need to write the information from the word sentences, into number sentences (or equations).
We are told that 150 tickets total are sold, so:
c+a=150 (child tickets plus adult tickets equal total tickets)
Next we are told that the total dollars is $1640. so:
c*8 + a*12 = 1640 (each child ticket times 8 dollars plus each adult ticket time 12 dollars = 1640 dollars)
The two equations then are:
8c+12a=1640
c+a=150
We can solve these equations several ways, the easiest is probably substitution. Solve c+a=150 for a
a=150 - c
then substitute that expression for a, in for a in the other equation
8c + 12a = 1640
8c + 12* (150-c) = 1640
8c + 1800 - 12c = 1640
-4c = -160
c=40
now we know that there were 40 children's tickets sold
going back to the simple first equation, we can then figure that 110 adult tickets were sold
answer is: child tickets=40, adult tickets=110
a quick check
40 child tickets at 8$ each is $320
110 adult tickets at 12$ each is $1320
1320+320=1640
hooray
keep at it
math is power
2007-01-21 13:15:59 · answer #2 · answered by enginerd 6 · 0⤊ 0⤋
If it is 12 for an adult and 8 for a child. You can buy 110 adult tickets which total $1320. The remaining money $320 can buy 40 child tickets.
110 Adult = $1320
40 Child = $320
TOTAL
150 tickets = $1640
2007-01-21 13:11:49 · answer #3 · answered by Lister55 1 · 0⤊ 0⤋
110 adult x 12 = 1320 and 40 childs x 8 = 320 and that 150 for $1640
2007-01-21 13:11:04 · answer #4 · answered by phyteacher 2 · 0⤊ 0⤋
I think this is what you want
12a+8c=1640
a+c=150
a=150-c
12(150-c)+8c=1640
1800-12c+8c=1640
1800-4c=1640
-4c=1640-1800
-4c=-160
c=40
plug that answer back into the equation
12a+8(40)=1640
12a-320=1640
12a=1320
a=110
110 Adult tickets; 40 childrens tickets
2007-01-21 13:04:28 · answer #5 · answered by Tiff 5 · 0⤊ 0⤋
12a+8c=1640 dicide both sides by 4
3a+2c=410
a+c=150 multiply by -2
-2a-2c=-300
3a+2c=410 add
a=110
110+c=150
c=40
110 adult tickets & 40 children tickets.
check
12*110=8*40=1320=320=1640
2007-01-21 13:05:11 · answer #6 · answered by yupchagee 7 · 0⤊ 0⤋
12a+8c=$1640 figure out a and c i have heard this many times on my tests but i forgot it sorry!
2007-01-21 13:07:12 · answer #7 · answered by JUDI 3 · 0⤊ 0⤋