Question

At the movie theatre, child admission is 6.30 and adult admission is 9.40. On Wednesday, 155 tickets were sold for a total sales of 1233.80. How many adult tickets were sold that day?

Answer 1

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Define x and y:
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Let x be the number of adult tickets sold.
Let y be the number of child tickets sold.

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Construct equations:
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There were 155 tickets sold
⇒ x+ y = 155

Total sales is $1233.80
⇒9.4x + 6.3y = 1233.8

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Solve for x and y:
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x + y = 155 ------------------ (1)
9.4x + 6.3y = 1233.8 --------------- (2)

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From equation 1:
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x + y = 155
x = 155 - y

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Sub x = 155 - y into equation 2:
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9.4 (155 - y) + 6.3y = 1233.8
1457 - 9.4y + 6.3y = 1233.8 . // Apply distributive property
1457 - 3.1y = 1233.8 // Combine like terms
1457 = 3.1y +1233.8 // Add 3.1y on both sides
233.2 = 3.1y // Subtract 1233.8 from both sides
72 = y // Divide by 3.1 on both sides
y = 72 // Make y the subject

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Sub y = 72 into equation 1:
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x + y = 155
x + 72 = 155 // Sub y = 72
x = 83 // Take away 72 from both sides


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Find the number of adult and child tickets sold:
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Adult = x = 83
Child = y= 72

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Answer: 83 Adult tickets were sold that day.
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