D asked in Science & MathematicsMathematics · 1 month ago

# math question?

The cost of a ticket to the circus is \$18.00 for children and \$33.00 for adults. On a certain day, attendance at the circus was 1,100 and the total gate revenue was \$30,300. How many children and how many adults bought tickets?

The number of children was (

) and the number of adult was (

)

Relevance
• 1 month ago

18*C+33*A =\$30300

C+A            =1100

divide by 100

18c+33a=303

use excel

c.........a..........#........\$

2.........9..........11.......333

3.........8..........11.......318

4.........7..........11.......303

400C+700A=1100 ppl& \$30300

• 1 month ago

Here's an intuitive way to solve this.

Let's say all 1,100 tickets were sold to children. If so, the circus would have made 1,100 * \$18 = \$19,800

But they actually made \$10,500 more than that:

\$30,300 - 19,800 = 10,500

For each ticket that is sold to an adult rather than a child, the circus makes an additional \$15.

\$33 - 18 = 15

Dividing we see the circus sold 700 adult tickets

10,500 / 15 = 700

The other 400 are child tickets.

700 adult tickets @ \$33 = 23,100

400 child tickets @ 18 = 7,200

---------- . . . . . . . . . . . . . . . -------------

1100 tickets . . . . . . . . . . \$30,300

• 1 month ago

Let C=the number of children; A=the number of adults.

C+A=1100

18C+33A=30300

=>

18C+33(1100-C)=30300

=>

15C=6000

=>

C=400

A=1100-400=700

• sepia
Lv 7
1 month ago

The cost of a ticket to the circus is \$18.00 for children and \$33.00 for adults.

On a certain day, attendance at the circus was 1,100

and the total gate revenue was \$30,300.

How many children and how many adults bought tickets?

x + y = 1100

33x + 18y = 30300

18x + 18y = 19800

15x = 10500

x = 700

y = 400

The number of children was (400)

and the number of adults was (700).

• Jeremy
Lv 6
1 month ago

c = number of children; a = number of adults.

System:

{c + a = 1,100 <=== Attendance on a certain day.

{18c + 33a = 30,300 <=== Total revenue on the same day (\$).

{c = 1,100 - a.

{18c + 33a = 30,300 ==> Recall "c = 1,100 - a" ==> 18(1,100 - a) + 33a = 30,300 ==>

==> 19,800 - 18a + 33a = 30,300 ==> 19,800 + 15a = 30,300 ==>

==> 15a = 30,300 - 19,800 ==> 15a = 10,500 ==> a = 10,500/15 = 700.

Hence: c = 1,100 - 700 = 400.

ANSWERS: The number of children was 400, and the number of adults was 700.

• Philip
Lv 6
1 month ago

c-ticket costs \$18, a-ticket costs \$33. Suppose

[c](c-tickets) were sold. Then [1100-c](a-tickets)

were sold. Total sales = \$[c](18) +\$[1100-c]33 =

\$(18c-33c+33000)=\$30,300., ie., 33000 -15c =

30300, ie., 15c = 33000-30300 = 2700, ie.,

30c = 5400, 3c = 540, c = 180. Then number

• 1 month ago

Number of children: c

On a certain day, attendance at the circus was 1,100: → a + c = 1100 → c = 1100 - a

…and the total gate revenue was \$30,300:

18c + 33a = 30300 → recall: c = 1100 - a

18.(1100 - a) + 33a = 30300

19800 - 18a + 33a = 30300

15a = 30300 - 19800

15a = 10500

a = 10500/15

a = 700

Recall: c = 1100 - a

c = 1100 - 700

c = 400