Can Anyone On Here Help Me Solve This Question Please?

[Elena_W]

The local soccer team club spent $675 on tickets to a professional soccer game. If the club bought three fewer $15 tickets than four-fifths the number of $12 tickets, how many tickets of each type did the club buy?

[Gizmonster]

30 tickets @ $12

and

21 tickets @ $15

[Gizmonster]

and if you need the working out:

Let x = number of $15 tickets and y = number of $12 tickets.

We have:

15x + 12y = 675

and:

x + 3 = (4/5)y ------> rearranging this gives 15x + 45 = 12y

Combine this with above equation gives:

12y - 45 + 12y = 675
24y = 675 + 45
24y = 720
y = 30

and

x + 3 = (4/5)30
x = 24 - 3
x = 21

[Elena_W]

i dont understand how you got the 45

[Gizmonster]

Take the equation:

x + 3 = (4/5)y

and multiply both sides by 15, gives:

15x + 45 = 12y

Hope that helps.
Any more questions, feel free to ask :)

[Elena_W]

Thank you so much for your help! But what's the reason behind multiplying both sides by 15?

[fiction-factory]

You could choose 5 instead of 15 but you'd still get the same answer

[fiction-factory]

5x +15 =4y
But by using 15 it makes the x coefficient of both equations the same

[Elena_W]

The 15 i'm multiplying to both sides is just the $15 dollar tickets right?

[Gizmonster]

I needed 15x in the equation, so I could substitute it into the original equation.

We have:

15x + 45 = 12y. Re arranging gives, 15x = 12y - 45

Now in the original equation, we have:

15x + 12y = 675

So instead of writing 15x, we put 12y - 45 in its place, so:

12y - 45 + 12y = 675

Rearranging this gives 24y = 720 -----> y = 30

[fiction-factory]

>The 15 i'm multiplying to both sides is just the $15 dollar tickets right?

You can multiply both sides of an equation by any number and the equality still applies. 15 was chosen by Gizmonster for the reason he has now given, but he could have chosen any number that eliminated the fractions (as it's easier to deal with whole numbers) , but Gizmonster's aproach made it easier to solve the simultaneous equations in one step

[fiction-factory]

This may help
http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/simultaneoushirev1.shtml

[Elena_W]

Thank you so much for your help!! I had been trying to figure this out for so many hours and had asked everyone, but no one knew the answer! Once again thanks so much!

[Elena_W]

Thank you fiction-factory as well, i really appreciate your help as well!!