Question

On the first day of ticket sales the school sold 6 adult tickets and 2 child tickets for a total of $98.The school took in $182 the second day by selling 13 adult tickets and 2 child tickets.What is the price each of one adult ticket and one child ticket?

Answer 1

ok. for this one, we need to set up a system of equations. we will let the price of the adult tickets be A, and the price of the child tickets be C.
with the first part of the problem, we know that 6 adult tickets (6A) and 2 child tickets (2C) is 98. this equation would be 6A+2C=98.
we follow the same idea in the next part of the problem. 13A+2C=182
so, our system of equations is:
6A+2C=98
13A+2C=182

Answer 2

how did you get 98 on the first one?

Answer 3

the 98 is the total they made on the first day- its the $98 (unless im totally blind and reading it wrong)

Answer 4

haha no your right,so then what will be my next step?

Answer 5

a stands for adult tickets
c stands for child tickets

6a + 2c = 98 --> (-1)6a + 2c = 98
13a + 2c = 182
----------------
-6a - 2c = - 98 (result of multiplying by -1)
13a + 2c = 182
---------------add
7a = 84
a = 12

now sub 12 in for a in either equation...
13a + 2c = 182
13(12) + 2c = 182
156 + 2c = 182
2c = 182 - 156
2c = 26
c = 13

check...
6a + 2c = 98
6(12) + 2(13) = 98
72 + 26 = 98
98 = 98 (correct)

you can check it by the other equation as well...

13a + 2c = 182
13(12) + 2(13) = 182
156 + 26 = 182
182 = 182 (correct)

ANSWER : Adult tickets cost $ 12 and child tickets cost $ 13

Answer 6

@texaschic101 how did you get -1 on the first line>

Answer 7

I multiplied the first equation by a -1 to cancel out the c's

Answer 8

or you could have multiplied the second equation by a -1 and that would have cancelledout the c's as well

Answer 9

like @texaschic101 posted, you solve the system of equations.
multiplying by the -1 is another way of writing what we did in the last one, where we used subtraction. its to get a positive and negative value of the C.

Answer 10

but what im trying to ask is why -1,why couldnt it of had been another integer?

Answer 11

look at your other integer.....if you wanted to cancel out the a's you would have to find a number that 6 and 13 would both go into. You want to try to pick the easiest integer. Do you understand ? morganashley is better at explaining then I am....I can just do it, but not good at explaining it.

Answer 12

multiplying by -1 gets a -2c in one equation, so when it is added to the next equation, it is eliminated. i hope this helps. Nice to meet you, Texaschic101!