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For a school play. Jim sold 6 adult tickets and 15 student tickets and collected $48. Adam sold 8 sdult tickets and 7 student tickets and collected $38. Find the prices adult and students tickets?


any help would be nice
 
I always wonder why students post problems like this with absolutely no effort shown. Is there not a teacher out there who actually introduces some vague concept of solutions? No one EVER told you to DEFINE a few things?

I'll get you started with the very most important step. Surprisingly, it is also the easiest.

A = Price of an Adult Ticket
S = Price of a Student Ticket

You tell me what's next.
 
then i went 14a+22s=$86
but seein how i dont know what im doin looks wrong to me
 
First, notice that the only WRITTEN definitions are in UPPER Case. No one knows what lowercase letters mean.

You are losing information when you combine the students' sales. Consider each student's sales separately.
 
Help is here!

Use the Matrix function on your graphing calculator;

JIM 6a + 15s = $48 [6 15 48] [1 0 3]
Adam 8a + 7s = $38 [8 7 38] [0 1 2]

Answer: The Adult tickets are $3 / The student tickets are $2
<Or, the hard way...>---------------------------------------------------------

System Elimination

8(6a+15s=48) -6(8a+7s=38)
48a+120s=384 -48a-42s=-228
-combine the like terms-
78s=156
s=2--------------------------------------
7(6a+15s=48) -15(8a+7s=38)
42a+105s=336 -120-105s=-570
-combine the like terms-
-78a=-234
a=3-------------------------------------

I hope this helps. Good Luck ;-)
 
We still don't know what 'a' and 's' mean. Really, someone should define them.
 
Re: Help is here!

librachia said:
Use the Matrix function on your graphing calculator;

JIM 6a + 15s = $48 [6 15 48] [1 0 3]
Adam 8a + 7s = $38 [8 7 38] [0 1 2]

Answer: The Adult tickets are $3 / The student tickets are $2
<Or, the hard way...>---------------------------------------------------------

System Elimination

8(6a+15s=48) -6(8a+7s=38)
48a+120s=384 -48a-42s=-228
-combine the like terms-
78s=156
s=2--------------------------------------
7(6a+15s=48) -15(8a+7s=38)
42a+105s=336 -120-105s=-570
-combine the like terms-
-78a=-234
a=3-------------------------------------

I hope this helps. Good Luck ;-)
Click to expand...


in the elimination part how did you get the equations like that where does the 8 and - 6 come from confueses me
 
Re: Help is here!

System Elimination

8(6a+15s=48) -6(8a+7s=38)
48a+120s=384 -48a-42s=-228
-combine the like terms-
78s=156
s=2--------------------------------------
7(6a+15s=48) -15(8a+7s=38)
42a+105s=336 -120-105s=-570
-combine the like terms-
-78a=-234
a=3-------------------------------------

I hope this helps. Good Luck ;-)[/quote]


in the elimination part how did you get the equations like that where does the 8 and - 6 come from confueses me[/quote]

You have two equations, one for each person selling tickets:
6A + 15S = 48
8A + 7S = 38

Now -- you want to add the equations together and eliminate one of the variables. To do that, you have to have numbers that cancel out by one of the variables. You get to choose which variable you want to eliminate, and you choose numbers to multiply the equations by to achieve that.

For example, if you multiply the first equation by 8 and the second one by -6, then your top equation will be "48A +120S = 388..." and the bottom one will be "-48A - 42S = -228...". When you add those together the A terms will cancel out.

That's how the example solution was done by Librachia.

Once you have found S, then you replace S in one of your equations by that number and work out what value A has.
 
Gezzzzz brandon...get rid of your video games...

A = price of Adult ticket
S = price of Student ticket ...... are you ok with this ?

Ok; you're TOLD:
"Jim sold 6 adult tickets and 15 student tickets and collected $48."
So 6 adult tickets cost $6A and 15 student tickets cost $15S ; got that?
Since those total $48, then:
6A + 15S = 48 : clear? Now divide each term by 3:
2A + 5S = 16 [1] : still with me?

You're also told:
"Adam sold 8 sdult tickets and 7 student tickets and collected $38."
So, going at it like with Jim, we have:
8A + 7S = 38 [2] : easy, right?

So now we have 2 equations:
2A + 5S = 16 [1]
8A + 7S = 38 [2]

Multiply equation [1] by 4; so now we have:
8A + 20S = 64 [1]
8A + 7S = 38 [2]

Do you see why we multiplied by 4?
Reason is to get the A terms to be the same: 8A.
We could have made the S terms the same instead,
by multiplying [1] by 7 and [2] by 5: but always take the easier option.

Now subtract [2] from [1]:
8A - 8A + 20S - 7S = 64 - 38
13S = 26
S = 26 / 13 = 2 : 2 bucks for Student tickets

Substitute that in [1] or in [2] to get the value of A : DO IT!!

Note: you're lucky I'm in a good mood this morning; my grandson Tyler
was selected last night to be on the Bantam (ages 12 and 13) basketball team
to represent Ottawa East; well, he got 171 of the 542 points his league team
scored in 9 games so far, so THEY better have picked him, else the pickers
would have heard from this grandpa in no uncertain terms 8-)
 
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