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Engineer1
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 13 Jan 2024, 20:11
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lpetroski
For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long?

A. 2.00 + [ \(\frac{0.75r}{2}\) ]
B. 2.00 + 0.75[ \(\frac{r}{2}\) ]
C. 2.00 + 0.75[ r ]
D. 2.00 + [1.5r ]
E. 2.00 + 0.75 [ 2r]
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chetan2u KarishmaB MartyMurray

Hi All, I did it correctly in my practice test 6. And I understand that in 5.5 miles, it would be 11 half miles, and in 5.7 it will be 12 half miles.
I also solved the kind of problems before similar to the sentence below, but just not together as it is in this problem. I got the answer of my calculation as E, so I checked it. But I could not figure out where the below sentence fit in. Is it because 5.7 means 6? Well, even without this sentence, the problem does not change, I guess. Any clarification is highly appreciated.

Thank you!

for every number x, [ x ] is defined to be the least integer greater than or equal to x,
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 13 Jan 2024, 20:46
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lpetroski
For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long?

A. 2.00 + [ \(\frac{0.75r}{2}\) ]
B. 2.00 + 0.75[ \(\frac{r}{2}\) ]
C. 2.00 + 0.75[ r ]
D. 2.00 + [1.5r ]
E. 2.00 + 0.75 [ 2r]


chetan2u KarishmaB MartyMurray

Hi All, I did it correctly in my practice test 6. And I understand that in 5.5 miles, it would be 11 half miles, and in 5.7 it will be 12 half miles.
I also solved the kind of problems before similar to the sentence below, but just not together as it is in this problem. I got the answer of my calculation as E, so I checked it. But I could not figure out where the below sentence fit in. Is it because 5.7 means 6? Well, even without this sentence, the problem does not change, I guess. Any clarification is highly appreciated.

Thank you!

for every number x, [ x ] is defined to be the least integer greater than or equal to x,
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It is because r need not be an integer.

Say he traveled 0.6 miles. The cost he incurred is 2$ as fixed charge and 0.75$ for first 0.5 miles and another 0.75$ for remaining 0.1 miles.
Total becomes 2+2*0.75 = 3.5$

Now, if we did not have [x], the answer would be 2+0.75*(2*0.6) = 2.9$, which will be wrong.
The answer is 2+0.75[2*0.6] = 2+0.75*2 = 3.5$

So, [] is ensuring that you have miles in multiples of 1/2 mile.
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 11 Jun 2025, 11:28
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Instead of going the route of formula, take a random number, lets say 2.1 miles.

To get the number of half miles in 2.1, multiply it by 2, which gives 4.2, Now [4.2] is the integer GREATER than of EQUAL to 4.2 which will be 5, thus total charge is 2+ 0.75[2r]

Pitfall answer. If we take [r] first and then convert to half miles, then here 2.1 becomes 3 and half miles will be 6, which is not what the question stem is asking for.

Hope I am able to clarify.

lpetroski
For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long?

A. 2.00 + [ \(\frac{0.75r}{2}\) ]
B. 2.00 + 0.75[ \(\frac{r}{2}\) ]
C. 2.00 + 0.75[ r ]
D. 2.00 + [1.5r ]
E. 2.00 + 0.75 [ 2r]
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 11 Jun 2025, 22:07
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long?

A. 2.00 + [ \(\frac{0.75r}{2}\) ]
B. 2.00 + 0.75[ \(\frac{r}{2}\) ]
C. 2.00 + 0.75[ r ]
D. 2.00 + [1.5r ]
E. 2.00 + 0.75 [ 2r]

Hi, people, let's get into this!

First, think of a random distance (e.g. 5.4 miles) and manually figure out the cost based on the prompt: $10.25

Then, see which of the options would spit out a similar value, keeping in mind the [x] condition. Remember, we’re looking for an equation that will give us more than $10 so (A), (B), and (C) are clearly out therefore.

When we look at (D) and (E),

(D) spits out 2 + [1.5 x 5.4] or 2 + [8.1]: $11

(E) is the answer therefore and we can also check it: $2 + $0.75 [2 (5.4)] = $2 + 0.75 (11) = $10.25

Note: Being a little extra careful and testing two distance values can be prudent.
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For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 29 Oct 2025, 16:49
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Fixed cost is $2
Extra variable pay:
If you cover 1/2 mile, you pay$0.75
If you cover n such 1/2 miles, you pay $0.75n
How many such 1/2 miles did you cover? That is r / (1/2) = 2r times
If 2r is a fractional value, we need the next higher integer, i.e. [2r]
ex. if r = 2.4, number of 1/2 miles = 2.4/(1/2) = 4.8 i.e. 5, which is [4.8]

Total = 2 + 0.75[2r] ... (E)

lpetroski
For each trip, a taxi company charges a fixed fee of $2.00 plus $0.75 for each 1/2 mile or fraction of 1/2 miles. If, for every number x, [ x ] is defined to be the least integer greater than or equal to x, then which of the following represents the company's charge, in dollars, for a trip that is r miles long?

A. 2.00 + [ \(\frac{0.75r}{2}\) ]
B. 2.00 + 0.75[ \(\frac{r}{2}\) ]
C. 2.00 + 0.75[ r ]
D. 2.00 + [1.5r ]
E. 2.00 + 0.75 [ 2r]
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