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# If a taxi driver charges x cents for the first quarter-mile of a trip

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If a taxi driver charges x cents for the first quarter-mile of a trip  [#permalink]

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22 Jan 2015, 07:46
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55% (hard)

Question Stats:

75% (02:03) correct 25% (02:13) wrong based on 163 sessions

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If a taxi driver charges x cents for the first quarter-mile of a trip and (x/5) cents for each additional quarter-mile, what is the charge, in cents, for a trip whose distance in miles is the whole number y?

A. (x+xy)/125

B. (4x + 4xy)/5

C. (4x+xy)/500

D. (4x+xy)/5

E. xy/25

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Re: If a taxi driver charges x cents for the first quarter-mile of a trip  [#permalink]

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22 Jan 2015, 08:07
Bunuel wrote:
If a taxi driver charges x cents for the first quarter-mile of a trip and (x/5) cents for each additional quarter-mile, what is the charge, in cents, for a trip whose distance in miles is the whole number y?

A. (x+xy)/125

B. (4x + 4xy)/5

C. (4x+xy)/500

D. (4x+xy)/5

E. xy/25

let Y be 1 mile
x= 20 cents

as per given info
in 1 mile we have 4 quarter mile
so for the first mile x=20 cents and x/5 cents =20/5=4 cents for every additional quarter mile
so total =20+4+4+4=32 cents charge for complete ride.

we just substitute our values in the given options and we get our ans B.
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Re: If a taxi driver charges x cents for the first quarter-mile of a trip  [#permalink]

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28 Jan 2015, 00:26
Answer = B. (4x + 4xy)/5

Let y = 1, which constitutes total 4 quarters

1st quarter cost = x

Remaining 3 quarters cost $$= \frac{3x}{5}$$

Total cost $$= \frac{3x}{5} + x = \frac{8x}{5}$$

Placing y = 1 in the OA, only option B fits in
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Re: If a taxi driver charges x cents for the first quarter-mile of a trip  [#permalink]

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28 Jan 2015, 06:50
ans ..B..
total quarters miles in y miles=4y...
cost @x/5 cents= 4xy/5 cents...
in this total, first quarter is x cents... so add x and subtract x/5..
ans 4xy/5+4x/5
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Re: If a taxi driver charges x cents for the first quarter-mile of a trip  [#permalink]

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27 Jun 2015, 02:33
I tried to solve in the following manner, but my values are satisfying option D, i want to know where am i going wrong.

x= 5 cents
y= 4 mile
For the first mile, charge should be x(5 cents) and for the remaining 3 miles charge should be x/5 or 1 cent for each mile.
Total charge= 5 cents + 1 cent *(3 miles) = 8 cents

Answer choice D, (4x + xy)/5 gives 8 cents and hence i marked D, however answer B is correct.

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Re: If a taxi driver charges x cents for the first quarter-mile of a trip  [#permalink]

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27 Jun 2015, 06:28
ash99 wrote:
I tried to solve in the following manner, but my values are satisfying option D, i want to know where am i going wrong.

x= 5 cents
y= 4 mile
For the first mile, charge should be x(5 cents) and for the remaining 3 miles charge should be x/5 or 1 cent for each mile.
Total charge= 5 cents + 1 cent *(3 miles) = 8 cents

Answer choice D, (4x + xy)/5 gives 8 cents and hence i marked D, however answer B is correct.

Hi ash99,
your method is correct but you have not understood the Q properly..
the prices are for quarter mile and not for entire mile..
so taking the values as you have decided..
total charge=5+(4*3*1(4*3 is the number of quarter in last 3 milesand 1 cent is the price)+3*1(3 is the number of quarter in first mile as the first Quarter of it has the price 5 , which has already been considered)....=20..
B should fit in
hope it helped
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Re: If a taxi driver charges x cents for the first quarter-mile of a trip  [#permalink]

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31 Jan 2016, 11:34
y=1 mile, x=5 cents and x/5=1 cent. so y trip will cost 8 cents. plug in x and y and solve in 30 secs. B
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Re: If a taxi driver charges x cents for the first quarter-mile of a trip  [#permalink]

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11 Jun 2016, 02:32
In y miles,how many 1/4 miles are there?

y/(1/4)=4y.

Now for 1 part of y,the charge is x cents.

So remaining parts or 4y-1=(4y-1)*x/5=4xy-x/5

Total charge=x+4xy-x/5= 4xy+4x/5
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Re: If a taxi driver charges x cents for the first quarter-mile of a trip  [#permalink]

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28 Aug 2017, 06:54
not too difficult if you understand conceptually and plug in #s.

consider x=10 (easily div by 5).
lets also pick y=4 (keep small number to avoid long calculations)

mile 1 = x + (3)*($$\frac{x}{5}$$).
- this is b/c the question tells us the rate is x for the first ($$\frac{1}{4}$$) mile and x/5 for each additional $$\frac{1}{4}$$ mi
- Ans: 10c + 3*2c = 16c for Mile 1

every additional mile = 4*2c = 8c

4 miles = 16 + 3(8) = 40c total
-> KEY: Plug in x=10 & y=4 into A/C to see WHICH GIVE YOU 40

B: $$\frac{40+160}{5}$$ = 40
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Re: If a taxi driver charges x cents for the first quarter-mile of a trip  [#permalink]

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31 Aug 2017, 10:17
Bunuel wrote:
If a taxi driver charges x cents for the first quarter-mile of a trip and (x/5) cents for each additional quarter-mile, what is the charge, in cents, for a trip whose distance in miles is the whole number y?

A. (x+xy)/125

B. (4x + 4xy)/5

C. (4x+xy)/500

D. (4x+xy)/5

E. xy/25

Since 1 mile has 4 quarter-miles, a trip of y miles has 4y quarter-miles, and after the first quarter-mile that charges x cents, there are 4y - 1 additional quarter-miles that charge x/5 cents each. Thus, the total cost is:

x + (x/5)(4y - 1)

5x/5 + (4xy - x)/5

(4x + 4xy)/5

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Re: If a taxi driver charges x cents for the first quarter-mile of a trip &nbs [#permalink] 31 Aug 2017, 10:17
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