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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: 58060
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% (02:01) correct 22% (02:05) wrong based on 77 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: 22 Dec 2014 Posts: 4 Re: Miguel took a taxi to the airport and paid$2.50 to start plus $0.25 p [#permalink] ### Show Tags 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] ### Show Tags 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: 294 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] ### Show Tags 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

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]

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18 Feb 2015, 01:55
2

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 !!!!! So, the answer is E.... SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1768 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 $$x = \frac{5}{0.25} + 30 = 50$$ _________________ Kindly press "+1 Kudos" to appreciate Math Expert Joined: 02 Sep 2009 Posts: 58060 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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