SOLUTION: there were 405 tickets sold. cardholders tickets are $1.25 and non-cardholders tickets are $2.50. total amount collected was $713.75. how many of each kind were sold?

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Question 951687: there were 405 tickets sold. cardholders tickets are $1.25 and non-cardholders tickets are $2.50. total amount collected was $713.75. how many of each kind were sold?
Found 2 solutions by macston, stanbon:
Answer by macston(5194) (Show Source):
You can put this solution on YOUR website!
c=cardholders tickets; n=non-cardholders tickets
c+n=405
c=405-n
$1.25(c)+$2.50(n)=$713.75 Substitute for c.
$1.25(405-n)+$2.50(n)=$713.75
$506.25-$1.25(n)+$2.50(n)=$713.75 Subtract $506.25 from each side.
$1.25(n)=$207.50 Divide each side by $1.25.
n=166 ANSWER 1:There were 166 non-cardholder tickets sold
c=405-n=405-166=239 ANSWER 2: There were 239 cardholder tickets sold.
CHECK:
$1.25(c)+$2.50(n)=$713.75
$1.25(239)+$2.50(166)=$713.75
$298.75+$415.00=$713.75
$713.75=$713.75

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
there were 405 tickets sold. cardholders tickets are $1.25 and non-cardholders tickets are $2.50. total amount collected was $713.75. how many of each kind were sold?
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Quantity Eq:: o + t = 405 tickets
Value Eq::: 125o + 250t = 71375 cents
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Modify::
125o + 125t = 125*405
125o + 250t = 71375
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Subtract and solve for "t"::
125t = 20750
t = 166 (# of 2.50 tickets sold
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Solve for "o"::
o + t = 405
o + 166 = 405
o = 239
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Cheers,
Stan H.
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