Answer
$$x=255$$ $$y=105$$
Work Step by Step
Let $x$ be the number of seats in the orchestra section and $y$ be the number of seats in the balcony section.
Equation 1: $x+y=360$
Equation 2: $45x+35y=15150$
We can solve for the numbers using the substitution method.
Using equation 1, subtract $y$ from both sides:
$$x+y=360$$ $$x+y-y=360-y$$ $$x=360-y$$
Substitute this equation to equation 2:
$$45x+35y=15150$$ $$45(360-y)+35y=15150$$ $$16200-45y+35y=15150$$ $$16200-10y=15150$$
Subtract $16200$ from both sides:
$$16200-16200-10y=15150-16200$$ $$-10y=1050$$
Divide both sides by $-10$:
$$\frac{-10y}{-10}=\frac{1050}{10}$$ $$y=105$$
Substitute this value of $y$ to equation 1:
$$x+105=360$$
Subtract $105$ from both sides:
$$x+105-105=360-105$$ $$x=255$$
Use equation 2 to check:
$$45x+35y=15150$$ $$45(255)+35(105)=15150$$ $$11475+3675=15150$$ $$15150=15150$$
