SOLUTION: I've tried many times to find the answer... and I've also never had a real big thing for math that's why I'm in summer school right now... If I could get any help at all it would

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I've tried many times to find the answer... and I've also never had a real big thing for math that's why I'm in summer school right now... If I could get any help at all it would       Log On


   

Question 3402: I've tried many times to find the answer... and I've also never had a real big thing for math that's why I'm in summer school right now... If I could get any help at all it would be great, and maybe a brief x-pla. on how it's to be done
"A theater sells children's tickets for $4 and adult tickets for $7. One night 575 tickets worth $3575 were sold.
How many adults and children bought tickets"
Thanks Many
Matt McIvor
Found 3 solutions by drglass, pannalal, ehull:
Answer by drglass(89) About Me  (Show Source):
You can put this solution on YOUR website!
Basically the same way you would solve otherwise.

3x-2.5y=7.125

2.5x-3y=7.3125

You should eleminate x or y and there is no particular advantage in picking one or the other in this case. So, let's pick x and use elimination:

Multiply the first equation by -2.5%2F3 and we get:



Now add this to the second equation and we get

-%282.75%2F3%29y+=+1.375

Divide either side by -2.75/3 and we get y = -1.5. Substitute this value of y in to the first equation and we get x = 1.125.

It is important to verify these numbers using the original equations:

3x-2.5y=7.125 and

2.5x-3y=7.3125

become
3(1.125)-2.5(-1.5) = 3.375 + 3.75 = 7.125 and

2.5(1.125)-3(-1.5) = 2.8125 + 4.5 = 7.3125

Answer by pannalal(9) About Me  (Show Source):
You can put this solution on YOUR website!
First convert decimal into fractions:
So, first equation becomes:
3x+-+5y%2F2+=+57%2F8
On multiplying both sides by 8:
24x+-+20y+=+57

and, second equation becomes:
5x%2F2+-+3y+=+117%2F16
on multiplying both sides by 16:
40x+-+48y+=+117
Now, equations are:
24x+-+20y+=+57 ... (1)
40x+-+48y+=+117 ... (2)
Solve in usual steps to get x = 9/8 and y = -3/2

Answer by ehull(1) About Me  (Show Source):
You can put this solution on YOUR website!
The problem asks you to find the number of children tickets which we can call c, and the number of adult tickets, or (a).
After establishing the variables, set up an equation to show the relationship between a and c. C + A = 575 tickets This first equation helps to show the relationship between the amount of tickets.
It is also important to consider the cost of the tickets. $4*C + $7*A = $3575
The cost of $4 per children's ticket, and &7 per adult ticket is shown through multiplication. Each ticket is multiplied by the cost per ticket. The total being $3575 dollars in all.
Solve the first equation for one of the variables.
C + A = 575 C = 575 - A The number of children's tickets is the total number of tickets 575 take away the number of adult tickets.
Solve the second equation, by SUBSTITUTING the (C) for what it equals: 575 - A
$4 * C + $7*A = $3575
$4*(575-A) + $7*A = $3575
Solve by multiplying the $4 dollars by both numbers in parentheses.
$4*575 - $4*A + $7*A = $3575
$2300 - $4A + &7A = $3575
Next, Combine like terms - $4A + $7A= $3A
$2300 + $3A = $3575
Solve the 2 step equation. First, subtract $2300 from both sides.
$2300-$2300 + $3A = $3575 - $2300
$3A = $1275
Second, divide both sides by $3.
$3A $1275
--- = ------
$3 $3
A = 425
Now, use the A = 425 to find out what C equals.
Go back to the first equation we wrote: C + A = 575
C + 425 = 575 Therefore C = 150, because 150+425=575
The answer then, is 425 adult tickets and 150 children's tickets
Check the answer by plugging in the number of tickets into the second equation
$4*C + $7*A = $3575
$4*150 + $7*425 = ?
$600 + 2975 = $3575