Airplane ticket price calculation

[mkxc3]

Hey I'm in the National 5 Maths and we just got this homework, I tried multiple algebraic expressions to find the price of each but to no avail. Please help
''100 people are on a plane. Some people have tickets for $70 and some have tickets for $50. The total raised sum from the plane tickets was $6240. How many people bought $70 seats, and how many people bought $50 seats?''

 

[MarkFL]

Hello, and welcome to FMH!

What did you try that didn't work?

 

[mkxc3]

Hello, and welcome to FMH!

What did you try that didn't work?

I did a couple of things that just didn't work heh..
50x+70y=6240
if x= 1, then
50+70y=6240
70y=6190
y=88.4285......
obv this doesn't work
then I 'came up' with this:
100=50x +70y
if x= 1 then...
100=50+70y
50=70y
so 50 people bought $70, but then if I did if y=1 then 30 people would have bought $50 tickets which sums up to 80 in total, so what about the other 20 haha..
I am probably making it more difficult than it actually is, so please help with untangling the mess I made

 

[MarkFL]

This equation is good:

[MATH]50x+70y=6240[/MATH]
And I would divide by 10 to get:

[MATH]5x+7y=624[/MATH]
Now, we also know that the total number of passengers is 100, so we may write:

[MATH]x+y=100[/MATH]
Now we have two equations in two unknowns, and an exact solution can be obtained...can you proceed?

 

[mkxc3]

simultaneous equation! haha immediately rang to my mind once I saw it, thanks! 62 would have $70 tickets and 38 would have tickets fro $50

 

[MarkFL]

Yes, I got the same solution.