Problem Solving Question. Pretty Please help.

Tickets to a school concert cost $4.50 for an adult and $3 for a child. if a total of 120 adults AND children attended the concert and $420 was collected, calculate the number of children who attended the concert.

No. of children—x:
$4.50(120 - x) + $3x = $420 Multiply each side by 2/3 to avoid decimals
3(120 - x) + 2x = 280
360 - 3x + 2x = 280
x = 80

Answer: 80 children

Let the number of ticket for adult and children be x and y respectively

given total number of ticket is 120

x+y=120

further given cost of adult ticket is 4.5 and children is 3

so we have second equation as

4.5x+3y=420

x+y=120

we will solve this two equations

let's multiply ii by 3 and subtract from i we got

4.5x+3y=420

3x+3y=360

1.5x=60

x=40
when we plug x=40 in equation x+y=120

we got y=80

so number of children ticket is 80 and number of adult ticket is 40

let
'x' be the number of adults attended
'y' be the number of children attended

So the equations we can formulate from the problem are:
eq 1.
x+y=120,
x = 120 - y

eq 2.
(4.5)x + 3y=420


Solution:
since: x = 120 - y

(4.5)x + 3y=420
(4.5)(120-y) + 3y = 420
540 - (4.5)y + 3y = 420
540 - 420 = (4.5)y - 3y
120 = 1.5y
y = 80 --->number of children attended
x = 40 ---> number of adults attended

a: number of adults
c: number of children

a + c = 120 (number of adults and children totals 120)
a = 120 - c

4.5*a + 3*c = 420 (you pay 4.5 for each a and 3 for each c and in total you pay 420)
use a = 120 - c in this equation
4.5*(120-c) + 3*c = 420
540 - 4.5*c + 3*c = 420
1.5*c = 120
c = 80

I'll use a for the number of adults and c for the number of children.
4.5a + 3c = 420
a + c = 120
Multiply the second equation by 3.
3a + 3c = 360
Subtract this from the first equation.
1.5a = 60
a = 40
c = 80
Check: 40*$4.50 + 80*$3 = $420
So 80 children attended.