math question?

Question

A local theme park had 840 vistors last weekend and collected a total of 11640 from admission tickets . If an adult's admission ticket is 18 dollars and a child's ticket is 12 dollars, how many adults and how many children visited the park?

Answer 1

18x+12y=11640
840-x=y

18x+12(840-x)=11640
18x+10080-12x=11640
6x=1560
x=260 adult tickets
y=580 childrens tickets

Answer 2

Let

x = Children

y = adults

840 = total children and adults

12x = Children price of the tickets

18y = Adults price of the tickets

11640 = Total admission recieved

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The equations

x + y = 840- - - - - - - - -Equation 1
12x + 18y = 11640- - - -Equation 2

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Substitute method equation 1

x + y = 840

x + y - x = 840 - x

y = 840 - x

The answer is y = 840 - x

Insert the y value into the equation 2

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12x + 18y = 11640

12x + 18(840 - x) = 11640

12x + 15120 - 18x = 11640

- 6x + 15120 = 11640

- 6x + 15120 - 15120 = 11640 - 15120

- 6x = - 3480

- 6x/- 6x = - 3480 / - 6x

x = 580. . .Number of Children

The answer is x - 580

Insert the x value into equation 1

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x + y = 840

580 + y = 840

580 + y - 580 = 840 - 580

y = 260. . . . Number of adults

The answer is y = 260

Insert the y value into equation 1

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Check for equation 1

x + y = 840

580 + 260 = 840

840 = 840

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Check for equation 2

12x + 18y - 11640

12(580) + 18(260) = 11640

6960 + 4680 = 11640

11640 = 11640

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The solution set is { 580. 260 }

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There were 260 adults

There were 580 Children

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Answer 3

let the no of adults be a and the no of children be c
the equations will be
18a+12c=11640
dividing by 6
3a+2c=1940
a+c=840 *-2
-2a-2c=-1680
3a+2c=1940
adding
a=260
sub c=580