University thearter sold 463 tickets for a play. Tickets cost $24 per adult and $12 per senior citizen. If total receipts were $7224, how many senior citizen tickets were sold?
2007-10-31 05:52:43 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Put the amount of tickets per adult at X
That makes the amount of tickets per senior 463-X
24X+(463-X)*12 = 7224
2X + 463 - X = 7224/12 = 602
X + 463 = 602
X = 602 - 463 = 139
So 139 tickets for adults (at 24$) and 463-139=324 for seniors (at 12$)
2007-10-31 05:59:54 · answer #1 · answered by Mich90 2 · 2⤊ 0⤋
let
a = adult tickets
s = senior citizen tickets
463 = Total adult and senior citizen tickets
24a = cost of adults tickets
12s = cost of senior citizen tickets
7224 = Total receipts
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Substitution Method
a + s = 436- - - - - - - - - Equation 1
24a + 12s = 7224- - - - Equation 2
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Isolate s variable in equation 1
a + s = 436
Transpose a
a + s - a = - a + 436
s = - a + 436
Substitute the s value in equation 2
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24a + 12s = 7224
24a + 12( - a + 436) = 7224
Distributive property
24a + (- 12a + 5556) = 7224
Remove parenthesis
24a - 12a + 5556 = 7224
Collect like terms
12a + 5556 = 7224
Transpose 5556
12a + 5556 - 5556 = 7224 - 5556
Collect like terms
12a = 1668
Divide both sides of the equation by 12
12a / 12 = 1668 / 12
a = 1668/12
a = 139. . . â. .Number of adults tickets sold
Substitute the a value into equation 1
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a + s = 436
139 + s = 436
Transpose 139
139 + s - 139 = 436 - 139
s = 324. . .â. .Number of senior citizens tickets
Substitute the s value into equation 1
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Check for equation 1
a + s = 436
139 + 324 = 436
436 = 436
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Check for equation 2
12a + 24s = 7224
12139) + 24(324) = 7224
3336 + 3888 = 7224
7224 = 7224
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Both equations balance
There are 324 Senior citizens Tickets sold.
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2007-10-31 13:21:34 · answer #2 · answered by SAMUEL D 7 · 0⤊ 0⤋
OK
Here is how you can do it
24x + 12y = 7224
x + y = 463 ; multiply bottom equation by 12
24x + 12y = 7224
12x + 12y = 5556 ; now subtract bottom from top (note y's go away)
12x = 1668
x = 139
So there were 139 adult tickets.
Substitute
x + y = 463
139 + y = 463
y = 324
SO there were 324 senior citizen tickets.
Check
24(139) + 12 (324) = 7224??
3336 + 3888 = 7224??
7224 = 7224 YES
Hope that helps.
2007-10-31 13:29:35 · answer #3 · answered by pyz01 7 · 0⤊ 0⤋
x=adult
y=senior
x+y = 463
24*x +12*y = 7224
X = 463-y
24(463-y) + 12*y = 7224
12*y = 3888
Y = 324 ( Number of seniors bought tickets)
X = 139 (Number of adults bought tickets)
2007-10-31 13:12:45 · answer #4 · answered by Mohsen J 2 · 0⤊ 0⤋
System of equations, baby!
2007-10-31 13:00:24 · answer #5 · answered by ? 6 · 0⤊ 1⤋