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A taxi company charges $1.75 for the first

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NandishSS Master | Next Rank: 500 Posts Default Avatar
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A taxi company charges $1.75 for the first

Post Sun Jul 16, 2017 6:01 am
A taxi company charges $1.75 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90?

A. 4 miles
B. 4 (1/4) miles
C. 4 (3/4 )miles
D. 5 (1/2) miles
E. 6 (1/4) miles

OA: D

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Post Sun Jul 16, 2017 11:25 am
NandishSS wrote:
A taxi company charges $1.75 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90?

A. 4 miles
B. 4 (1/4) miles
C. 4 (3/4 )miles
D. 5 (1/2) miles
E. 6 (1/4) miles
We can PLUG IN THE ANSWERS, which represent the greatest distance someone could travel with $4.90.
Since the question stem asks for the maximum possible distance, start with the greatest answer choice.
When the correct answer choice is plugged in, the total cost of the trip will not exceed $4.90.

E: 6.25 miles
Cost of the first quarter-mile = $1.75.
Remaining distance = (total distance - first quarter) = 6.25 - 0.25 = 6 miles = 24 quarter-miles.
At a rate of 15 cents per quarter-mile, the cost of the remaining 24 quarter-miles = (24)(15) = 360 cents = $3.60.
Total cost = (cost of the first quarter-mile) + (cost of the remaining quarter-miles) = $1.75 + $3.60 = $5.35.
The total cost is too great.
Eliminate E.

D: 5.5 miles
Cost of the first quarter-mile = $1.75.
Remaining distance = (total distance - first quarter) = 5.5 - 0.25 = 5.25 miles = 21 quarter-miles.
At a rate of 15 cents per quarter-mile, the cost of the remaining 21 quarter-miles = (21)(15) = 360 cents = $3.15.
Total cost = (cost of the first quarter-mile) + (cost of the remaining quarter-miles) = $1.75 + $3.15 = $4.90.
Success!

The correct answer is D.

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Post Sun Jul 16, 2017 1:29 pm
I would test the answer choices, as Mitch has done. You could also use algebra here, though.

The formula for this type of word problem: Total cost = (fixed cost) + (rate)(variable cost)


In this case: T = 1.75 + (0.15)(x - 1), where x = total # of quarter-miles. We'll have to convert that to miles later.

4.90 = 1.75 + 0.15(x - 1)
4.90 = 1.75 + 0.15x - 0.15
4.90 = 1.5 + 0.15x
3.40 = 0.15x
340 = 15x
x = 22 2/3

22 2/3 quarter-miles is slightly greater than 5.5 miles (22/4) and slightly less than 5.75 miles (23/4).

This question assumes that distance can only be in perfect quarter-miles with no fractional charges. Assuming that, then 5.5 miles is the maximum distance one could travel. The answer is D.

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Post Sun Jul 16, 2017 1:37 pm
Another easy way to solve would be to create a chart to ballpark:



We can see that 4.90 will cover over 5 miles, but not 6. We just then have to test whether 5.5 works, as Mitch did.

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Post Sun Jul 16, 2017 2:01 pm
NandishSS wrote:
A taxi company charges $1.75 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90?

A. 4 miles
B. 4 (1/4) miles
C. 4 (3/4 )miles
D. 5 (1/2) miles
E. 6 (1/4) miles

OA: D
Let's follow the money

Start with $4.90

The taxi company charges $1.75 for the first quarter of a mile
So, after 0.25 miles, we've spent $1.75

$4.90 - $1.75 = $3.15

So, we have $3.15 remaining, and we've traveled 0.25 miles so far.

The taxi company charges $0.15 for each additional 0.25 miles
In other words, for every $0.15, we can travel 0.25 miles
$3.15/$0.15 = 21

So, our remaining $3.15 will buy us 21 additional 0.25-mile advances.
(21)(0.25) = 5.25 miles

TOTAL DISTANCE = 0.25 + 5.25 = 5.5 miles

Answer: D

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Post Sun Jul 16, 2017 6:53 pm
Hi NandishSS,

Since the answers are NOT nice 'round' numbers, you can use a variation on TESTing THE ANSWERS - but instead of using the answers that are given, you can use round numbers to eliminate options.

We're told that the first 1/4 mile costs $1.75 and each additional 1/4 mile costs $0.15. We're asked for the maximum distance that could be traveled for $4.90

Based on the answer choices, I'll start with what a 5 mile trip cost...
The first mile would cost $1.75 + 3($0.15) = $2.20
Each additional mile would cost 4($0.15) = $0.60
So a 5 mile trip would cost $2.20 + 4($0.60) = $2.20 + $2.40 = $4.60

Since we're dealing with $4.90, we will clearly end up going more than 5 miles (so we can eliminate Answers A, B and C)... but we wouldn't travel that much more than 5 miles... From here, it's fairly easy to determine that the additional $0.30 would get us an extra 1/2 mile.

Final Answer: D

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Post Sun Jul 23, 2017 5:40 pm
1.75 + .15q = 4.90

subtract 1.75:

.15q = 3.15

multiply by 100:

15q = 315

divide by 15:

q = 21

So we could travel an extra 21 quarter miles, or 5.25 miles. Adding the first 1/4 mile to the trip (the one for which we paid $1.75), we have a total of 5.50 miles.

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Post Tue Jul 25, 2017 11:08 am
NandishSS wrote:
A taxi company charges $1.75 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90?

A. 4 miles
B. 4 (1/4) miles
C. 4 (3/4 )miles
D. 5 (1/2) miles
E. 6 (1/4) miles
We can let x = the number of ¼-miles traveled with $4.90 and create the following equation:

1.75 + 0.15(x - 1) = 4.90

175 + 15x - 15 = 490

160 + 15x = 490

15x = 330

x = 22

We see that 22 quarter-miles can be traveled with $4.90 and 22 x ¼ = 5 ½ miles.

Answer: D

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