Math question?

Question

Adult tickets for a play cost $20 and child tickets cost $5. If there were 22 people at a performance and the theater collected $335 from ticket sales, how many children attended the play?

Answer 1

Substitution Method

Let

c = child

a = adult

22 = total children and adults

5c = cost of a child ticket

20a = cost of a adult ticket

335 = total collected

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c+ a = 22- - - - - - - -Equation 1
5x + 20a = 335- - - Equation 2
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Isolate a in equation 1

c + a = 22

Transpose c

c + a - c = - c + 22

a = - c + 22

Substitute the a value into equation 2
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5c + 20a = 335

5c + 20( - c + 22) = 335

The distributive property

5c + (- 20c + 440) = 335

Remove parenthesis

5c - 20c + 440 = 335

Collect like terms

- 15c + 440 = 335

Transpose 440

- 15c + 440 - 440 = 335 - 440

Collect like terms

- 15c = - 105

Divide both sides of the equatio by - 15

- 15c / - 15 = - 105 / - 15

c = - 105 / - 15

c = 7. . .Number of children

Insert the c value into equation 1
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c + a = 22

7 + a = 22

Transpose 7

7 + a - 7 = 22 - 7

Collect like terms

a= 15

Insert the a value into equation 1
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Check for equation 1

c + a = 22

7 + 15 = 22

22 = 22

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Check for equation 2

5c + 20a = 335

5(7) + 20(15) = 335

35 + 300 = 335

335 = 335
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Both eqjuations balance

7 children attended the play

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Answer 2

let no. of adults be x and no. of children be y.
Therefore x + y = 22 (total no. who attended)
and 20x+5y = 335. ($20 per adult ticket + $5 per child ticket = total money collected)
You now have two equations you can solve simultaneously, if you know how on a calculator. If not, rearrange the first one to give : x = 22 - y
You can now put this into the 2nd equation to give
20(22-y) +5y = 335
therefore 440 -20y+5y = 335
440 -15y= 335
-15y = 335-440
-15y = -105
y = -105/-15
y= 7
Therefore 7 children attended