Question

Ron and kathy are ticket-sellers at their class play, ron handling student tickets that sell for $1.00 each and kathy selling adult tickets for $3.50 each. if their total income for 26 tickets was $46.00, how many did ron sell?

Answer 1

Let's create two equations and solve them using the substitution method.

`\left \{ {{s ~+ ~a ~= ~26} \atop {s~+~3.5a~ = ~46}} \right.`

• where s = student tickets and a = adult tickets.

Solve the first equation for s. Subtract a from both sides.

1. s = 26 - a

Plug s into the second equation.

1. (26 - a) + 3.5a = 46
2. Combine like terms.
3. 26 + 2.5a = 46
4. Subtract 26 from both sides.
5. 2.5a = 20
6. Divide both sides by 2.5.
7. a = 8

Plug 8 for a into the first equation.

1. s + (8) = 26
2. Subtract 8 from both sides.
3. s = 18

Since Ron handled student tickets, he sold 18 tickets (s = student tickets = 18).