The school is selling tickets to a play. Tickets cost $3 and $5 for adults. If $245 is collected on the sale of 65 tickets. How many adult and student tickets were sold?

Answer 1

1. Label Child as " C " , Adult - as " A"
2. Set up the two equations

C + A = 65

3C + 5A = 245

There are two ways to solve ( Elimination or substitution)

Substitution method :

C= 65 - A

Plug C= 65-A into 3C+5A=245

3(65-A)+5A=245

195-3A+5A=245

2A=50

A=25 (Adult)

C= 65-25= 40(Child)

Elimination method ;

C + A = 65

3C + 5A = 245

Either C or A of Coefficient makes same number but opposite sign.

-3(C+A)=-3(65)

3C+3A=195

Now, We set up a system of equations

-3C-3A=-195

3C + 5A = 245

Add two equations

2A= 50

A=25(Adult)

C= 40(child)

Answer 2

C+A =65

3C+5A = 245

multiply 1st by 3

3C+3A =3(65)=195

subtract last from 2nd

2A = 50

divide both sides by 2

A =25 Adults

C= 65-25= 40 Children