# Admission tickets to a local circus show were priced at USD4 for adult and USD3 for the student.

Admission tickets to a local circus show were priced at 4 dollars for adult and 3 dollars for the student. For the first 3 days of the show, 810 tickets were sold and the total receipts were $2853. How many of the each type of ticket were sold?

**Solution:**

Based on the details given in the problem, we can have this variable representation:

**= adult tickets**

*x***= student tickets**

*y*Given the conditions in the problem, we can derive the following equations

**+**

*x***= 810 [Eq. 1]**

*y*[

*The sum of the adult and student tickets is 810*]4

**+ 3***x***= 2853 [Eq. 2]***y*[

*The total sales of the adult and the student tickets is 2853*]Solving Eq. 1 for x gives:

**+**

*x***= 810**

*y***= 810 – y [Eq. 3]**

*x*Substituting Eq. 3 in Eq. 2 gives:

4

**+ 3***x***= 2853 [Eq. 2]***y*4(810 –

**) + 3***y***= 2853***y*3240 – 4

**+ 3***y***= 2853***y*3240 –

**= 2853***y*3240 – 2853 =

*y* 387 =

*y*Using Eq. 1 to solve for x gives:

**+**

*x***= 810**

*y***+ 387 = 810**

*x***= 810 – 387**

*x***= 423**

*x*Therefore, there were

**423**adult tickets sold and**387**student tickets sold.Check:

**+**

*x***= 810**

*y*423 + 387 = 810

810 = 810

4

**+ 3***x***= 2853***y*4(423) + 3(387) = 2853

4(423) + 3(387) = 2853

1692 + 1161 = 2853

2853 = 2853