Question

The circus sold 1,000 tickets. Adult tickets cost $8.25, children's tickets cost $4.75, and a total of $6,048.50 was collected. How many tickets of each kind were sold? The number of adult tickets is _____.

Answer 1

Answer:

Number of adult tickets is 371

Explanation:

Let us assume the number of adult tickets sold is x

                               number of children's tickets sold is y

We have the following simultaneous equations:

(1) x + y = 1000

(2) 8.25x + 4.75y = 6048.5

Substitue the value of x from equation (1) (x = 1000-y) into equation (2), we have the following equation:

8.25 x (1000-y) + 4.75y = 6048.5

8250 - 8.25y + 4.75y = 6048.5

--> 3.5y = 2201.5

--> y = 629  --> x = 1000 - 629 = 371

Number of adult tickets sold is  371. Number of children tickets sold is 629.

Answer 2

Answer:

The number of adult tickets is 371.

The number of children's tickets is 629

Explanation:

Let A be the number of adult tickets sold and C be the number of children's tickets sold. The following linear system can be modeled based on the information provided:

$A+C=1,000\\8.25A+4.75C=6,048.50$

Solving the linear system:

$8.25A -4.75A+4.75C-4.75C=6,048.50-4,750\\A=\frac{1,298.50}{3.5}\\A=371\\C=1000-371\\C=629$

The number of adult tickets is 371.

The number of children's tickets is 629.