Help With Word Problem

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watcjpp

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Ticket Sales: Tickets for a concert were sold to adults for $3 and to students for $2. If the total recipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold.

I have to use the substitution method to solve. I am not sure where or how to begin?

The question asks me how many of each were sold?

X=Adult Tickets
Y=Student Tickets

Would I begin like this? I am confused... :oops:

2x+1y=824
 
I think it might help if you stated clearly what your variables, expressions, and equations mean, what they stand for, where they came from. For instance, what does "2x + 1y" stand for?

Eliz.
 
X=Adult Tickets @ $3
Y=Student Tickets @ $2

X=3
Y=2

WI begin like this for this problem if I am trying to find how many adult tickets were sold and how many student tickets were sold using the substitution method?

2(X)+2(Y)=184
 
So you are assuming, in the beginning, that you have sold three adult tickets and two student tickets...?

Eliz.
 
I see what you are saying. I am trying to find out how many adult tickets I have sold if I sold two times as many as I sold student tickets. I have spent about five hours trying to figure this out and I am not very good with word problems. I am also a 44 year old student who is finishing up there degree and I am a little rusty :oops: . I am really wondering am I supposed to divide the $824 by $6 to get what twice the amount would be? I appreciate you trying to help me.
 
watcjpp said:
I am really wondering am I supposed to divide the $824 by $6....
Click to expand...
Where is "$6" coming from? Neither of the tickets is priced at six dollars.

You need to get in the habit of defining your terms and using clear labelling. You say "x = Adult tickets" and "x = 3", which says that "I have sold three adult tickets". I don't think this is what you mean, and the cryptic notation is part of what is causing your confusion.

Instead, try something like this:

. . . . .number of adult tickets: a
. . . . .number of student tickets: s

(Note that the variable names are chosen to help me remember what each stands for.)

. . . . .Then a = 2s.

. . . . .cost of an adult ticket: 3
. . . . .cost of a student ticket: 2

. . . . .The income from the sale of a given type of
. . . . .ticket is the product of the cost of that type
. . . . .of ticket and the number of that type sold.

. . . . .adult-ticket income: 3a
. . . . .student-ticket income: 2s

. . . . .Substituting:

. . . . .3a = 3(2s) = 6s

. . . . .total cost: ....

...and so forth, getting a linear equation in one variable, which you can then solve.

Eliz.
 
watcjpp said:
Ticket Sales: Tickets for a concert were sold to adults for $3 and to students for $2. If the total recipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold.
Click to expand...
x = number of adult tickets, y = number of student tickets;
then x = 2y (twice as many adults).

sales to adult: 2y * 3 = 6y
sales to students: y * 2 = 2y

6y + 2y = 824

Can you finish it?
 
thanks for the assistance I am going to begin working on this and see what I come up with. I again thank you.
 
6y + 2y = 824
8y=824
8y/8=824/8
Y= 103 x=2y is 103(2)=206
X=206
This is what I got y=103 Student Tickets sold
x=206 Adult Tickets sold
Because 103(2)+206(3)=824

I really do appreciate the help and I see why it is important to clairfy what I am trying to do. :)
 
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