SOLUTION: The total receipts for 900 tickets were 95000. If students paid 75php per ticket, and non-students paid 125php per ticket, how many student-tickets were sold?

Question 87822: The total receipts for 900 tickets were 95000. If students paid 75php per ticket, and non-students paid 125php per ticket, how many student-tickets were sold?
Found 2 solutions by checkley75, tutorcecilia:
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
s+ns=900 ns=900-s
75s+125ns=95000 now replace ns with (900-s) & solve for s
75s+125(900-s)=95000
75s+112500-125s=95000
-50s=95000-112500
-50s=-17500
s=-17500/-50
s=350 tickes sold to students &
900-350=550 tickets sold to ns.
proof
75*350+125*550=95000
26250+68750=95000
95000=95000
Answer by tutorcecilia(2152) (Show Source): You can put this solution on YOUR website!
Let x = students
Let y = non-students
x + y = 900
Let y = 900 - x
.
75x + 125y = 95,000
75x + 125 (900-x) = 95, 000 [Substitute (900-x) for (y) and simplify]
75x + 112,500 - 125x = 95,000 [simplify the terms]
75x + 112,500 - 125x = 95,000 [combine like-terms]
-50x + 112,500 = 95, 000 [solve for the x-term]
-50x + 112,500 - 1112,500 = 95,000 - 112,500
-50x = -17,500
-50x/-50=-17,500/-50
x=350
.
Plug (x=350) into the original equation and solve for the y-term
x+y=900
350-y=900
y= 550
.
Check by plugging in the x and y values into the second equation.
75x + 125y = 95,000
75(350) + 125(550) = 95,000 [simplify]
95,000=95,000 [checks out]

.

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