Let's create two equations and solve them using the substitution method.
[tex] \left \{ {{s~ +~ a ~= ~364} \atop {2s~+~4.5a~=~1175.5}} \right. [/tex]
- where s = student tickets and a = adult tickets.
Solve the first equation for s.
- Subtract a from both sides.
- s = 364 - a
Plug s into the second equation.
- 2(364 - a) + 4.5a = 1175.5
- Distribute 2 inside the parentheses.
- 728 - 2a + 4.5a = 1175.5
- Combine like terms.
- 728 + 2.5a = 1175.5
- Subtract 728 from both sides.
- 2.5a = 447.5
- Divide both sides by 2.5.
- a = 179
Plug 179 for a into the first equation.
- s + 179 = 364
- Subtract 179 from both sides.
- s = 185
Since Ron handled student tickets, he sold 185 tickets (s = student tickets = 185).
Let's check our work.
In the first equation, s + a = 364; let's plug in what we got for a and s into the equation.
This means we will plug in 179 for a and 185 for s.
185 + 179 = 364
189 + 179 does equal 364, so this means we are correct in solving this system of equations.
Hope this helped you^
