adult tickets to the fall play cost $8 and student tickets cost $4. the drama class sold 20 more adult…

adult tickets to the fall play cost $8 and student tickets cost $4. the drama class sold 20 more adult tickets than student tickets to the fall play. if the class collected $880 from ticket sales, how many adult tickets were sold? the drama class sold ______ adult tickets. the solution is

Answer

Explanation:

Step1: Define variables

Let $x$ be the number of student - tickets sold. Then the number of adult - tickets sold is $x + 20$.

Step2: Set up the equation

The total money from ticket sales is the sum of the money from adult - ticket sales and student - ticket sales. The money from adult - ticket sales is $8(x + 20)$ (since adult tickets cost $8$ dollars each), and the money from student - ticket sales is $4x$ (since student tickets cost $4$ dollars each). The total money is $880$ dollars. So the equation is $8(x + 20)+4x=880$.

Step3: Expand the equation

Expand $8(x + 20)$ to get $8x+160$. The equation becomes $8x + 160+4x=880$.

Step4: Combine like - terms

Combine $8x$ and $4x$: $12x+160 = 880$.

Step5: Isolate the variable term

Subtract 160 from both sides of the equation: $12x=880 - 160$, so $12x=720$.

Step6: Solve for $x$

Divide both sides by 12: $x=\frac{720}{12}=60$.

Step7: Find the number of adult tickets

Since the number of adult tickets is $x + 20$, substitute $x = 60$ into it. The number of adult tickets is $60+20=80$.