Tickets sold in advance for a play cost $3 each. Tickets sold at th edoor for the same play cost $5 each. If 100 tickets were sold for this play for a total of $460, how many tickets were purchased at the door?

Question

anonymous · Answer

Let the tickets sold in advance be x
And let the tickets sold at the edoor be y.

So, according to the question:

x + y = 100              (Because total 100 tickets were sold)

3x + 5y = 460         (Because total 100 tickets sold for $460)

Multiply first equation by 3,

3x + 3y = 300           ----------------1
3x + 5y = 460          -----------------2

Subtract them:

3y - 5y = 300 - 460

-2y = 160

2y = 160

Now can you find y???

anonymous · Answer

where did you get 3x+3y=300?

anonymous · Answer

I have just multiply 3 by my own so that the solving method becomes easy...

There is one more method to solve it..
Would you solve it on your own??
I will tell you the steps???

anonymous · Answer

sure, let's try it.

anonymous · Answer

Firstly, you should about this method..
This method is called SUBSTITUTION METHOD..

Now tell me what is the first equation???

anonymous · Answer

x+y=100?

anonymous · Answer

Yes, now find x from here..
can you do that??

anonymous · Answer

times it by 3, so it will be 3x+3y=300?

anonymous · Answer

No, i am saying from this equation can you eliminate x,

ie x + y = 100

What if I subtract y from both sides, then what will you get??

anonymous · Answer

like x+y=100
-x+y=100
y=100

anonymous · Answer

wait, y=-x+100?

anonymous · Answer

Good but here you have eliminated y..
But you can eliminate y also, there is nothing wrong in that...

y = -x + 100

S0, Can I write it as: y = 100 -x.

I have just reversed that nothing more..
Right???

anonymous · Answer

well its minues 100 now, not Plus

anonymous · Answer

100 is positive and x is negative..
See it with microscope..
Seen or not??

ha ha ha..

anonymous · Answer

okay

anonymous · Answer

So, put this value now in second equation:

what is the second equation??

anonymous · Answer

3x+5y=460 the orginainal equation

anonymous · Answer

Now in place of y put (100 - x)

can you do it or not??

anonymous · Answer

im trying to figure out what your saying

anonymous · Answer

See like this:

3x + 5(100 - x) = 460

3x + 500 - 5x = 460

-2x = 460 - 500

2x = 40

x = 20

And now y = 100 - x = 100 - 20, subtract it and get the answer...

anonymous · Answer

oh okay,t hank you!

anonymous · Answer

Welcome dear..