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ratio problem - need the way to solve it.

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ratio problem - need the way to solve it.

by ronik74 » Thu May 03, 2012 10:40 am
The monthly traveling expenses of John are partly constant and partly vary with the number of miles that he travels in a month. When he travels 150 miles the total traveling expenses are $800 and when he travels 180 miles the total traveling expenses are $900. Find the total monthly expenses in a certain month in which he traveled 300 miles.


please advice.

correct answers : (the correct one is D)

A. $1650

B. $1600

C. $1450

D. $1300


E. $1400
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by karthikchandru » Thu May 03, 2012 11:00 am
Let K -> constant in "$" which doesn't depend on the number of miles.
Let V -> constant in "$/mile" which depends on the number of miles.

From the problem, when John travels 150 miles, the total traveling expenses is $800. This can be written as:
K + 150V = 800 ...........(1)

Similarly, when he travels 180 miles:
K + 180V = 900 ...........(2)

Solving (1) and (2), we get K = 300 and V = 10/3.

Now, we need to find total expenses when he travels 300 miles:

K + 300V = 300 + 300(10/3) = 1300
Hence, (D)
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by aneesh.kg » Thu May 03, 2012 11:01 am
The problem does not specify the nature of variation of expenses with miles. Expenses is a function of miles but the nature of the function is not specified and that's why the problem has insufficient data.

A GMAT question will never be worded so vaguely.

Let me solve the problem anyway, assuming the variation of Expenses to be linear with miles.

Let
E = a + m*b
where E is expenses and m is number of miles, and
a and b are constants which we will determine.

800 = a + 150b
900 = a + 180b
From the above two equations,
b = 10/3
a = 300

Using the values of a and b to find Expenses when m = 300,
E = 300 + (10/3)*300
= 1300

[spoiler](D)[/spoiler] is the answer.
Aneesh Bangia
GMAT Math Coach
[email protected]

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