Question

Tickets are sold at $20 for an adult and $10 for students. If the total ticket sales was $12000 and 740 people attended the play, how many adults attended? Solve as linear equation

Answer 1

Explanation:

We can set up the linear equation as follows:

Let x represent the number of adults and y represent the number of students. Then, we have the following equations:

20x + 10y = 12,000 (total ticket sales)

x + y = 740 (total attendees)

We can solve for x as follows:

20x + 10y = 12,000

20x = 12,000 - 10y

x = (12,000 - 10y) / 20

Substituting this value for x into the second equation, we get:

(12,000 - 10y) / 20 + y = 740

y = 740 - (12,000 / 20)

Now we have two equations:

x = (12,000 - 10y) / 20

y = 740 - (12,000 / 20)

We can solve for x as follows:

x = (12,000 - 10y) / 20

x = (12,000 / 20) - (5y / 2)

x = 600 - 2.5y

Now we have two equations in the two unknowns x and y:

600 - 2.5y = (12,000 - 10y) / 20

2.5y = 11,990 / 20

y = 4,798

Substituting this value for y into the first equation, we get:

600 - 2.5(4,798) = (12,000 - 10(4,798)) / 20

600 - 11,990 = (12,000 - 47,990) / 20

-11,390 = -35,990 / 20

-11,390 = 1,469.5 / 2

-11,390 = 734.75

734