child tickets, variable = ‘c’

You know two things: the total amount sold

$7.50 a + $4.50 c = $540

and the total number of tickets

a + c = 80

Solve the second equation for one of the variables. Let’s do a, so a = 80 – c

plug a = 80 – c back into the first equation,

7.5 (80 – c) + 4.5 c = 540

(7.5 x 80) – 7.5 c + 4.5 c = 540

600 – 3 c = 540

600 – 540 = 3c (subtracted 540 and 3c from each side)

3c = 60

c = 20 (20 children’s tickets)

plug c back into the second equation to find out how many adult tickets

a + c = 80

a = 80 – c

a = 80 – 20

a = 60 (60 adult tickets)

Double check, does 60 x 7.5 and 20 x 4.5 add up to 540?

450 + 90 = 540

Yee Haw. 60 adult tickets and 20 child tickets.

(If you need to solve for two variables, you need to have two equations. Solve for one variable using the first equation, then plug the result of that back into the second and you have your solution.)

7.5X+4.5Y=540

if X+Y=80 then Y=-X+80

Plug in the equation for Y

7.5X+4.5(-X+80)=540

Distibute 4.5

7.5X-4.5X+360=540

Subtract 360 and combine the variables.

3X=180

Divide by 3

X=60

Plug X into the first equation

X+Y=80

60+Y=80

Subtract 60

Y=20

So, your final answer is that 60 adult ticks and 20 children’s tickets were sold

7.50x + 4.50y = 540

x + y = 80

Isolate x:

x = 80 – y

Sub in x value for first equation:

7.5(80-y) + 4.50y = 540

600 – 7.5y + 4.5y = 540

-3y = -60

y = 20

Sub y back into 2nd equation to get x:

x + 20 = 80

x = 60

Now you have the answer:

20 children, 60 adult

7.5X + 360 – 4.5X = 540

3X = 180

X = 60

80 – (60) = 20

So they bought 60 adult tickets at $7.50 and 20 child tickets at $4.50

7.5X + 360 – 4.5X = 540

3X = 180

X = 60

80 – (60) = 20

simple