A certain charity concert was attended by 863 persons. Some bought general admission tickets for 50 pesos each and the rest bought reserved seat tickets for 75 pesos each. The total amount of money collected from these tickets was 50,000 pesos. How many people bought reserved seat tickets?

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Answers

2014-10-06T19:37:15+08:00
Let 'x' be the number of persons w/ tickets @50 pesos
    'y' be the number of persons w/ tickets @75 pesos
x+y = 863  ----equation 1
50x + 75y = 50,000   ----equation 2
from equation 1
x + y = 863
x = 863 - y  ----equation 3
substitute equation 3 to equation 2
50(863-y) + 75y = 50,000
43,150 - 50y + 75y = 50,000
25y = 50,000 - 43,150
25y = 6,850
y = 274 persons
substitute to equation 1
x + y =863
x + 274 = 863
x = 863 - 274
x = 589 persons
therefore there are 274 persons who bought reserved seat tickets
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