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09 Aug 2017, 23:39
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A county fair sold 1,750 tickets, each of which was either an adult or children's ticket, and earned a total of $27,000. The fair earned 25% more from adult tickets than from children's tickets, but sold 25% fewer adult tickets than children's tickets. How much did a children's ticket cost?
A. $10
B. $12
C. $15
D. $20
E. $25
A. $10
B. $12
C. $15
D. $20
E. $25
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10 Aug 2017, 00:26
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Bunuel
A county fair sold 1,750 tickets, each of which was either an adult or children's ticket, and earned a total of $27,000. The fair earned 25% more from adult tickets than from children's tickets, but sold 25% fewer adult tickets than children's tickets. How much did a children's ticket cost?
A. $10
B. $12
C. $15
D. $20
E. $25
A. $10
B. $12
C. $15
D. $20
E. $25
Let the number of children tickets be c => c+0.75c = 1750
c = 1000 , adult tickets will be 750
price of children,adult ticket can be (10,12.5), (12,15),(15,75/4) (20,25), (25,125/4) from the given options
10*1000 + 12.5*750 = 19375
12*1000 + 15*750 = 23250
15*1000 + 75/4*750 = ~29000
20000 + 25*750 = 38750
No Answer
Please correct me.. i think some 25% more than means 20% less logic is in play but i am not able to get it
10 Aug 2017, 01:40
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Let c=No. of children's ticket sold, so (1750-c)= No. of Adult's ticket sold.
Now, Let p1= Cost of children's ticket sold and p2= Cost of Adult's ticket sold.
So,
cp1 + (1750-c)p2 = 27000..................(1)
Now, the fair earned 25% more from adult tickets than from children's tickets.
So cp1 = 1.25(1750-c)p2....................(2)
Using (1) and (2), we get
(1750-c)p2 (1+1.25) = 27000..................(3)
Also, Fair sold 25% fewer adult tickets than children's tickets.
So, c=.75(1750-c)...................(4)
Solving (4) we get c = 750. Using this and (3) we get p2 = 12 and using p2 value and (2), we get p1 = 20.
IMO Answer should be D
Now, Let p1= Cost of children's ticket sold and p2= Cost of Adult's ticket sold.
So,
cp1 + (1750-c)p2 = 27000..................(1)
Now, the fair earned 25% more from adult tickets than from children's tickets.
So cp1 = 1.25(1750-c)p2....................(2)
Using (1) and (2), we get
(1750-c)p2 (1+1.25) = 27000..................(3)
Also, Fair sold 25% fewer adult tickets than children's tickets.
So, c=.75(1750-c)...................(4)
Solving (4) we get c = 750. Using this and (3) we get p2 = 12 and using p2 value and (2), we get p1 = 20.
IMO Answer should be D
