Ticket price word problem, system of equations: 36 persons are going on a trip....

[jellyfishcluster]

I'm having trouble with following practice exam problem:

36 persons are going on a trip. Adult ticket was 150$ more expensive than children's ticket. Total price of sold adult tickets was 4000$ and total price of sold children's tickets was 2000$. I'm supposed to calculate the total amount of children on the trip.

This is what I've done so far:
(Amount of adults) + (Amount of children)=36
or x + y =36
(Amount of adults)(base ticket price + 150)=4000
or x(z+150)=4000
and
(Amount of children)(base ticket price)=2000
or y(z)=2000

Then I get confused and get all kinds of nonsensical answers and/or can't get rid of any variables and it feels I'm running in circles. I'm starting to wonder if there's simpler way to approach the problem. The worst part: I've already deduced the correct answer like days ago, but still can't seem to make sensible formula for it. I know it can't be this hard. Any help is greatly appreciated.

 

[stapel]

I'm guessing that this exercise was translated from another language. I've tweaked the text a bit, so it's in standard English.

Thirty-six people are going on a trip. Adult tickets are $150 more expensive than are children's tickets. The total revenue from adult tickets sold was $4,000, and the total revenue from children's tickets sold was $2,000. Calculate the total number of children going on the trip.

This is what I've done so far:
(Amount of adults) + (Amount of children)=36
or x + y =36

So "x" stands for "the number of adults going" and "y" stands for "the number of children going"...?

(Amount of adults)(base ticket price + 150)=4000
or x(z+150)=4000

(Amount of children)(base ticket price)=2000
or y(z)=2000

Then I get confused and get all kinds of nonsensical answers and/or can't get rid of any variables and it feels I'm running in circles.

Please reply showing what you've done. For instance, you started by solving the first equation for one of the variables in terms of the other; say, x = 36 - y. This left you with:

. . . . .\(\displaystyle (36\, -\, y)\, (z\, +\, 150)\, =\, 4,000\)

. . . . .\(\displaystyle yz\, =\, 2,000\)

You multiplied out the first equation, and did the obvious substitution from the second, solved for z in terms of y, plugged back into the second equation, and... then what?

Please be complete. Thank you!

 

[Otis]

Make up an example, like:
20 children @ $50 = $1000
10 adults @ $200 = $2000 : so total = $3000

Figure out the "how it works" : then apply to your problem.

I can't see how doing this would demonstrate back-substitution leading to a quadratic equation to solve. What method are you thinking of?

 

[Otis]

I misunderstood your first post. I thought you were suggesting to start out letting children=20 and adult price=200 (that is, no variables), and then see "how it works". Instead, you meant: follow stapel, but with "easier" numbers. I get it now.

 

[jellyfishcluster]

Thank you all, I finally solved it with the help of second post by Denis (and after a good night sleep). And yes, I'm not a native english speaker "Amount of" and "Number of" would translate to exact same word in my language. I try to keep the correct usage in mind from now on.