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

Question

3 years ago

5

1,000 and the total gate revenue was $24,800. How many children and how many adults bought tickets.

1 answer:

Evgesh-ka [11] · Answer 1 · 2022-07-12T13:26:56+03:00

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

$14(x+y=1000)\\14x+14y=14000\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(14x+32y)-(14x+14y)=24800-14000\\14x+32y-14x-14y=10800\\18y=10800\\$

Dividing both sides by 18

$\frac{18y}{18}=\frac{10800}{18}\\y=600$

Putting y=800 in Eqn 1

$x+600=1000\\x=1000-600\\x=400$

400 children and 600 adults bought tickets.

Keywords: linear equations, subtraction

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