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# Trucking transportation rates are x dollars per metric ton per kilomet

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Re: Trucking transportation rates are x dollars per metric ton per kilomet [#permalink]
I understand why the answer is E by using x·t·n
How to get to the multiplication using fractions? It's not in the format $$\frac{\frac{x}{t}}{n}$$ nor $$\frac{x}{\frac{t}{n}}$$
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Re: Trucking transportation rates are x dollars per metric ton per kilomet [#permalink]
HKD1710 wrote:
Trucking transportation rates are x dollars per metric ton per kilometer. How much does it cost, in dollars, to transport one dozen cars, which weigh two metric tons each, n kilometers by truck?

(A)$$\frac{x}{12n}$$
(B) $$\frac{x}{24n}$$
(C) $$\frac{xn}{24}$$
(D) $$12xn$$
(E) $$24xn$$

I followed this approach

x dollars per metric ton per kilometer.

1 km = x dollars / MT

Now back solve this

n km = x n dollars /MT

1 MT = x n dollars

2 MT = 2 x n dollars

Above will be cost for 1 car

1 car = 2 x n dollars

12 car = 24 x * n dollars.
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Re: Trucking transportation rates are x dollars per metric ton per kilomet [#permalink]
philipssonicare

Not sure if you're still trying to track down the answer to your question but breaking down the problem can help, rather than trying to apply the concept of 'per' and write as a fraction

From the q stem we know it costs:
1) $x per one ton 2)$x per one km

Then we're also given that we need to transport 24 tons (12 x 2). So we know already its going to cost us 24x based on tons alone. Then from the breakdown above we can say 1 ton : 1 km. Therefore, we will need to multiply 24x by n (not divide) in order to derive the total cost because of the one to one relationship btw tons and kms
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Re: Trucking transportation rates are x dollars per metric ton per kilomet [#permalink]
HKD1710 wrote:
Trucking transportation rates are x dollars per metric ton per kilometer. How much does it cost, in dollars, to transport one dozen cars, which weigh two metric tons each, n kilometers by truck?

(A)$$\frac{x}{12n}$$
(B) $$\frac{x}{24n}$$
(C) $$\frac{xn}{24}$$
(D) $$12xn$$
(E) $$24xn$$

Concept tested - Clarity of formulating Formula and Units

Total cost = Rate * No. of units.

If a truck carries a load of One metric ton for 1 km , it will charge = x dollars

Therefore, if it carries a load of (2X12) i.e 24 metric ton for n Kms , it will charge =>[ x (dollars)/(1ton)*(1km)]* 24 (ton) *n (Km)
Units( km and tons) will get cancelled , hence total cost = 24xn
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Re: Trucking transportation rates are x dollars per metric ton per kilomet [#permalink]
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Re: Trucking transportation rates are x dollars per metric ton per kilomet [#permalink]
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