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# Miguel took a taxi to the airport and paid $2.50 to start plus$0.25 p

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Math Expert
Joined: 02 Sep 2009
Posts: 60727
Miguel took a taxi to the airport and paid $2.50 to start plus$0.25 p  [#permalink]

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17 Feb 2015, 09:22
00:00

Difficulty:

35% (medium)

Question Stats:

78% (02:00) correct 22% (02:05) wrong based on 78 sessions

Miguel took a taxi to the airport and paid $2.50 to start plus$0.25 per mile. Sean took a different route to the airport and paid $2.50 plus$5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Sean's ride was 30 miles, how many miles was Miguel's ride? A. 10 B. 20 C. 30 D. 40 E. 50 Kudos for a correct solution. _________________ Intern Joined: 15 Jan 2015 Posts: 22 Re: Miguel took a taxi to the airport and paid$2.50 to start plus $0.25 p [#permalink] ### Show Tags 18 Feb 2015, 01:55 2 Miguel took a taxi to the airport and paid$2.50 to start plus $0.25 per mile. Sean took a different route to the airport and paid$2.50 plus $5.00 in bridge toll fees plus$0.25 per mile. If each was charged exactly the same amount, and Sean's ride was 30 miles, how many miles was Miguel's ride?

A. 10
B. 20
C. 30
D. 40
E. 50

Sean- total amount paid = 2.5+5+(.25*30) = 15

Miguel- lets take ride is x miles,
total amount paid = 15 = 2.5+(.25*x)
then, x = 12.5/0.25 = 1250/25 = 50

Alternate method - lets take Miguel took X miles to airport. (clearly X>30)
Difference of miles = X-30
so, (X-30)*.25 = 5 (amount paid for toll)
X-30 = 20
X = 50

Manager
Joined: 13 Dec 2013
Posts: 58
Location: Iran (Islamic Republic of)
Re: Miguel took a taxi to the airport and paid $2.50 to start plus$0.25 p  [#permalink]

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18 Feb 2015, 03:14
2

With a bit little different approach as guys wrote !!!

since the stem says both people incurred the same cost to reach the airport , we can take equal both sides

the first person incurred : 2.5$+ .25$ for each mile

the second person incurred : 2.5 $+ .25$ for each mile + 5 $for tools if we take those 2 condition equal , terms 2.5$ and .25 $from both sides are cancelled and only remains 5$ in one side...

so we can deduce in order to both side be equal , the side which is not pay 5 $must drove more and for each mile driving the side must pay .25$ so in order to cover 5 $, that person must drive 20 miles more than the other person. as we are told that the person who paid 5$ , drove 30 miles, so Miguel must have driven 30 + 20 = 50 Miles !!!!!

Intern
Joined: 22 Dec 2014
Posts: 4
Re: Miguel took a taxi to the airport and paid $2.50 to start plus$0.25 p  [#permalink]

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17 Feb 2015, 10:46
1
We know that both Miguel and Sean are heading to the same location, using different routes, but charged the same amount.

Miguel: 2.5+1/4(x)=Sean

Sean: 2.5+1/4(30)+5=(Total Cost of Sean's Trip)
Sean: 2.5+7.5+5=15 (Total Cost of Sean's Trip)

Knowing how much Sean paid for his trip, we can now calculate how far Miguel traveled by solving for x

Miguel: 2.5+1/4(x)=(Total Cost of Sean's Trip)
Miguel: 2.5+1/4(x)=15 (Total Cost of Sean's Trip)
Miguel: 2.5+1/4(x)=15-2.5
Miguel: 1/4(x)=12.5
Miguel: x=12.5*4=50
Intern
Joined: 31 Dec 2014
Posts: 8
Location: United States
Concentration: Marketing
GMAT 1: 700 Q44 V41
Re: Miguel took a taxi to the airport and paid $2.50 to start plus$0.25 p  [#permalink]

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17 Feb 2015, 16:31
1
Add 2 miles to Sean's base so it's $3 +$5. 28 miles remain, so divide 28 by 4 to get $7. So Sean spent$15
Add 2 miles to Miguel's base to get $3. He needs to spend$12 more. 12 x 4 = 48. Add the two miles from the beginning and get 50 miles.
E. 50
Senior Manager
Joined: 28 Feb 2014
Posts: 289
Location: United States
Concentration: Strategy, General Management
Re: Miguel took a taxi to the airport and paid $2.50 to start plus$0.25 p  [#permalink]

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17 Feb 2015, 17:08
1
Bunuel wrote:
Miguel took a taxi to the airport and paid $2.50 to start plus$0.25 per mile. Sean took a different route to the airport and paid $2.50 plus$5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Sean's ride was 30 miles, how many miles was Miguel's ride? A. 10 B. 20 C. 30 D. 40 E. 50 Kudos for a correct solution. let x=Miguel's distance in miles 2.50 + .25x = 7.50 + .25(30) .25x = 12.50 x=50 Answer: E SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1721 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Miguel took a taxi to the airport and paid$2.50 to start plus $0.25 p [#permalink] ### Show Tags 19 Feb 2015, 00:34 1 Answer = E = 50 Let Miguel travelled = x miles Both made the same expenditure, so 2.5 + 0.25x = 2.5 + 5 + 0.25*30 $$x = \frac{5}{0.25} + 30 = 50$$ Math Expert Joined: 02 Sep 2009 Posts: 60727 Re: Miguel took a taxi to the airport and paid$2.50 to start plus $0.25 p [#permalink] ### Show Tags 22 Feb 2015, 11:40 Bunuel wrote: Miguel took a taxi to the airport and paid$2.50 to start plus $0.25 per mile. Sean took a different route to the airport and paid$2.50 plus $5.00 in bridge toll fees plus$0.25 per mile. If each was charged exactly the same amount, and Sean's ride was 30 miles, how many miles was Miguel's ride?

A. 10
B. 20
C. 30
D. 40
E. 50

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Explanation: To express this relationship mathematically, we can say that M is what Miguel paid, m is the distance Miguel traveled (in miles) S is what Sean paid, and s is the distance Sean traveled (in miles). Converting the text in the problem to algebra yields:

For Miguel's trip: M = 2.50 + 0.25 * m

For Sean's trip: S = 2.50 + 5.00 +0.25 * s = 7.50 + 0.25 * s

M = S; s = 30

Setting M = S, gives:

2.50 + m4 = 7.50 +

Solve for m:

m/4 = 7.50 - 2.50 + s/4
m/4 = 5.00 + s/4
m = 20 + s

Plug in 30 for s to get m = 50; so the correct answer is E.
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Re: Miguel took a taxi to the airport and paid $2.50 to start plus$0.25 p  [#permalink]

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23 Dec 2018, 09:51
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Re: Miguel took a taxi to the airport and paid $2.50 to start plus$0.25 p   [#permalink] 23 Dec 2018, 09:51
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