Question

A ticket to a concert costs either $12 or $15. A total of 300 tickets are sold, and the total money collected is $4140 . The number of $12 tickets sold are?​

Answer 1

Answer:

Step-by-step explanation:

system of equations… so, in the first one, let x =amount of ticket A, let y = amount of ticket B.

So, x + y = 300 tickets

In equation two, we know $12 per ticket A, and $15 per ticket B, but we don’t know the amount of tickets.

So, $12x + $15y = $4,140.

So we can solve this using elimination, substitution, graphing it etc. etc.

I will use substitution, as I prefer that when I have one equation that is x +/- y =

so i prefer multiplying by 15, so I am going to solve for y.

x + y = 300

-x ……. -x

y = -x +300

No substitute the y value into the second equation…

$12x +$15(-x + 300) =$4,140.

so we distribute the 15

12x -15x + 4500 = 4140

combine like terms:

-3x +4500 = 4140

subtract 4500 from both sides

-3x = -360

divide both sides by -3

x = 120. So we know that there were 120 of tickets A bought

so we go back to our system and solve

x + y = 300, but use our newly acquired x value.

120 + y = 300

y = 180

So, 120 of ticket A, 180 of ticket B, and we could plug it in and get the same answer….. just for fun

12x + 15y = 4140

12 (120) + 15 (180)

1440 + 2700 = 4140.