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25 May 2016, 03:56
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Martin bought 10 concert tickets, some at the full price of $2.00 per ticket, and some at a discounted price of$1.60 per ticket. If he spent a total of $18.00, how many discounted tickets did he buy? A) 3 B) 4 C) 5 D) 6 E) 7 _________________ Manager Joined: 08 Aug 2015 Posts: 55 Re: Martin bought 10 concert tickets, some at the full price of$2.00 per  [#permalink]

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25 May 2016, 04:06
The total amount is $18. That means the number of tickets purchased for$1.60 must be such that they round up the overall cost of discounted tickets to an integer.

He can either purchase 5 tickets at $1.60 which would take the cost of discounted tickets to$8 or 10 tickets which would take the cost of discounted tickets to $16. Since we know what the overall cost was and the number of tickets sold, we can tell that he purchased 5 discounted tickets at$1.60 and 5 tickets at the usual price for $2 bringing the total cost to$18

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Re: Martin bought 10 concert tickets, some at the full price of $2.00 per [#permalink] ### Show Tags 26 May 2016, 01:46 Let x be the number of tickets he bought at$2 per ticket.

then 2x + (10-x)1.6 = 18

0.4x = 2 => x = 5

discounted tickets = 10 -x = 5

Ans : C
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Re: Martin bought 10 concert tickets, some at the full price of $2.00 per [#permalink] ### Show Tags 26 May 2016, 05:58 Bunuel wrote: Martin bought 10 concert tickets, some at the full price of$2.00 per ticket, and some at a discounted price of $1.60 per ticket. If he spent a total of$18.00, how many discounted tickets did he buy?

A) 3
B) 4
C) 5
D) 6
E) 7

Some easy ways to do -

1) weighted average method..
Average of all tickets = cost/number of tickets = 18/10 = 1.8...
now the prices are 2 and 1.6.... the average of all lies exactly between 2 and 1.6,
so the ratio is 1:1 or can be calculated as $$\frac{2-1.8}{1.8-1.6}$$ =1..
so equal numbers for both 10/2 = 5 each
C

2) Equation and number property -
1.6x +2y = 18...
18 and 2y are integer..
x has to be a multiple of 5 for 1.6 to be integer, so values are 5 and 10..
10 is not possible as total cost = $$10*1.6 = 16\neq{18}$$..

2) two linear equations-
x+y = 10
2x+1.6y = 18..
solve and you will get x and y as 5

C
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Re: Martin bought 10 concert tickets, some at the full price of $2.00 per [#permalink] ### Show Tags 26 May 2016, 07:50 Bunuel wrote: Martin bought 10 concert tickets, some at the full price of$2.00 per ticket, and some at a discounted price of $1.60 per ticket. If he spent a total of$18.00, how many discounted tickets did he buy?

A) 3
B) 4
C) 5
D) 6
E) 7

2n + 1.6 (10-n) = 18

2n-1.6n = 18-16
.4n=2
n=5

and 10-n= 5

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