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The cost of a ticket to the circus is $14.00 for children and $32.00 for adults. On a certain day, attendance at the circus was 1,000 and the total gate revenue was $24,800. How many children and how many adults bought tickets.

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400 children and 600 adults bought tickets.

Step-by-step explanation:

Given,

Cost of one child ticket = $14

Cost of one adult ticket = $32

Total attendance = 1000

Revenue generated = $24800

Let,

x be the number of children.

y be the number of adults.

According to given statement;

x+y=1000   Eqn 1

14x+32y=24800   Eqn 2

Multiplying Eqn 1 by 14

[tex]14(x+y=1000)\\14x+14y=14000\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](14x+32y)-(14x+14y)=24800-14000\\14x+32y-14x-14y=10800\\18y=10800\\[/tex]

Dividing both sides by 18

[tex]\frac{18y}{18}=\frac{10800}{18}\\y=600[/tex]

Putting y=800 in Eqn 1

[tex]x+600=1000\\x=1000-600\\x=400[/tex]

400 children and 600 adults bought tickets.

Keywords: linear equations, subtraction

Learn more about subtraction at:

  • brainly.com/question/547255
  • brainly.com/question/545947

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