math help......?

Question

Adult tickets for a play cost $14 and child tickets cost $4. If there were 27 people at a performance and the theater collected $298 from ticket sales, how many children attended the play?

Answer 1

A + C = 27
14xA + 4xC = $298
multiply 1st equation by -4 and add to 2nd equation to eliminate C
-4A -4C = -108
14A+4C = 298
10A = 190
A=19 and so C=8

Answer 2

Substitute Method

Let

a = adults

c = child

27 = total adults and children

14a = adults ticket cost

4c = childs ticket cost

298 = total collected

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a + c = 27- - - - - - - - -Equation 1
14a + 4c = 298- - - - -Equation 2
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isolate the c variable in equation 1

a + c = 27

transpose a

a + c - a = - a + 27

c = - a + 27

Substitute the c value into equation 2
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14a + 4c = 298

14a + 4(- a + 27) = 298

`14a + (- 4a + 108) = 298

Remove Parenthesis

14a - 4a + 108 = 298

Colledting like terms

10a + 108 = 298

Transpose 108

10a + 108 - 108 = 298 - 108

10a = 190

Divide both sides of the equatio by 10

10a / 10 = 190 / 10

a = 190 / 10

a = 19

Insert the a value into equation 1

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a + c = 27

19 + c = 27

Transport 19

19 + c - 19 = 27 - 19

c = 8

Insert the c value into equation 1
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Check for equation 1

a + c = 27

19 + 8 = 27

27 = 27

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Check for equation 2

14a + 4c = 298

14(19) + 4(8) = 298

266 + 32 = 298

298 = 298

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Both equations balance

There were 8 children that attended the play

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Answer 3

For this, all you have to do is make two equations with two unknowns.

First, you'd make the equation for the money. In total, you have 298, and in order to get that, the number of children must have been multiplied by 4 and the number of adults must have been multiplied by 14, and then both those numbers must have been added together to give you 298. In mathematical words:

14x + 4y = 298

where x is the number of adults and y is the number of children. You also know that there were a total of 27 people at the play. So the number of adults plus the number of children is 27. that is,

x + y = 27

So now you have two equations with two unknowns. You can do a simple substitution here, just set y to equal 27 - x, and substitute that in the first equation to get:

14x + 4(27 - x) = 298

Then it should be peachy from there:

14x + 108 - 4x = 298
10x + 108 = 298
10x = 190
x = 19

and in order to now get the number of children, you solve x+y=27 and so you get

y=8

and that's your number of children that attended the play.

Answer 4

let a be the number of adult tickets and c be the number of children tickets

there are 27 people including adults and children
a + c = 27

adult tickets cost 14 and children tickets cost 4. The total of 298

14a + 4c = 298


a + c = 27
a = 27 - c


14(27 - c) + 4c = 298
378 - 14c + 4c = 298
-10c = -80
c = 8


there were 8 children

Answer 5

Let let adults be x
Let children be 27 - x

14x + 4(27-x) = 298
14x + 108 - 4x = 298
10x + 108 = 298
10x = 190
x = 19

therefore there were 19 adults
therefore there were 27 - 19 = 8 children

the answer is 8 children attended the play.