At a carnival, $2,914.25 in receipts were taken at the end of the day. The cost of a child's ticket was $20.50, an adult ticket was $29.75, and a senior citizen ticket was $15.25. There were twice as many senior citizens as adults in attendance, and 20 more children than senior citizens. How many children, adult, and senior citizen tickets were sold?

"x" children tickets are 70, "y" adult tickets 50 and "z" senior citizen tickets 25

Step-by-step explanation:

With the information of the statement we can pose the following equations:

we have to "x" children tickets, "y" adult tickets and "z" senior citizen tickets.

20.5*x + 29.75*y + 15.25*z = 2914.25

we also have to:

z = 2*y

plus that:

x = z + 20, replacing, we have left:

x = 2*y + 20

now, we replace each other in the main equation:

20.5 * (2*y + 20) + 29.75*y + 15.25 * (2*y) = 2914.25

41*y + 410 + 29.75*y + 30.5*y = 2914.25

101.25*y = 2504.25

y = 2504.25/101.25

y = 24.73

z = 2*24.73 = 49.46

x = 2*24.73 + 20

x = 69.46

"x" children tickets are 70, "y" adult tickets 50 and "z" senior citizen tickets 25

Children tickets = 69.4667

Adult tickets = 24.7333

Senior tickets = 49.4667

(The decimal does not make sense as we cannot have a fractional amount of tickets, but with the information given, this is the correct answer)

Step-by-step explanation:

Let's call the amount of children C, the amount of adults A and the amount of seniors S. Then, we can write the following system of equations:

C*20.5 + A*29.75 + S*15.25 = 2914.25 (eq1)

S = 2*A (eq2)

C = S + 20 (eq3)

Using eq2 in eq3, we have:

C = 2*A + 20 (eq4)

Using eq2 and eq4 in eq1, we have:

(2*A + 20) * 20.5 + A*29.75 + 2*A*15.25 = 2914.25

41*A + 410 + 29.75*A + 30.5*A = 2914.25

101.25*A = 2504.25

A = 2504.25 / 101.25 = 24.7333

Now using eq2, we have:

S = 2*A = 49.4667

And using eq4, we have:

C = 2*A + 20 = 69.4667

(The decimal does not make sense as we cannot have a fractional amount of tickets, but with the information given, this is the correct answer)