tickets cost $14 adult and $2 for kids?

Question

270 tickets sold and total was $2340, how many of each type sold?

Answer 1

a is the number of adult tickets; k is the number of child tickets.

The total number of tickets sold (a + k) is 270:

a + k = 270

The total amount raised ($14 times the number of adult tickets sold + $2 times the number of kids' tickets sold) was $2340:

14a + 2k = 2340

Solve first equation for k:

k = 270 - a

Plug into second equation and solve for a:

14a + 2(270 - a) = 2340
14a + 540 - 2a = 2340
12a = 2340 - 540 = 1800
a = 1800/12 = 150 adult tickets

Then use that and the first equation to compute the number of child tickets:

k = 270 - 150 = 120 child tickets.

Double check:

150 adult tickets + 120 child tickets = 270 tickets

$14 times 150 adult tickets + $2 times 120 child tickets = $2100 in adult tickets + $240 in child tickets = $2340 overall

check!

Answer 2

Suppose there were a adult tickets.
Then there were 270 - a kids' tickets ........(1)
14a + 2(270 - a) = 2340
14a + 540 - 2a = 2340
12a = 1800
a = 1800 / 12 = 150.
There were 150 adult tickets, and from (1) there were 270 - 150 = 120 kids' tickets.

Answer 3

150 adult tickets,
120 child tickets

let x = number of adult tickets sold
let y = number of child tickets sold
14x + 2y = 2340
x + y = 270

You need to take one equation and isolate a variable
x + y = 270
x = 270 - y

Now substitute that variable into the other equation and solve
14x + 2y = 2340
14(270 - y) + 2y = 2340
3780 - 14y + 2y = 2340
- 12y = - 1440
y = 120

Now take the value just found and plug it into either equation
x + y = 270
x + (120) = 270
x = 150

Answer 4

x+y=270

14x+2y=2340

x=270-y

14(270-y)+2y=2340
3780-14y+2y=2340
-12y+3780-3780=2340-3780
-12y=-1440
-12y/-12=-1440/-12
y=120 kids tickets

x+y=270
x=150 adult tickets

150*14=2100
120*2=240
2100+240= 2340