What equation am I looking for?

SweetDee93

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Jul 9, 2019
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3
Hi there, I feel really stupid :( word problems confuse me...

I am working on weighted averages and I am not sure how to translate part of my question into a formula to solve...

A motorist purchases gas as follows:
56 litres at 0.99/litre
64 litres at 1.065/litre
54 litres at 1.045/litre

I have already solved for the average number of litres of gas purchased, as well as the average cost per litre. The next question is if you average 8.75km per litre, what is the average cost of gasoline per km?

I'm not asking for anyone to solve it for me... I just want to know what I do with this information in order to solve it... Thanks!
 

Dr.Peterson

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Nov 12, 2017
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4,156
Taking simpler numbers for the moment, suppose that gas costs $2 per liter (sorry, I'm American!), and you can drive 3 km per liter. Then with one liter, you go 3 km at a cost of $2. What is the cost per kilometer?

What you will have done there is to divide ($/liter)/(km/liter) = $/km. The liters cancel.
 

SweetDee93

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\(\displaystyle
Taking simpler numbers for the moment, suppose that gas costs $2 per liter (sorry, I'm American!), and you can drive 3 km per liter. Then with one liter, you go 3 km at a cost of $2. What is the cost per kilometer?

What you will have done there is to divide ($/liter)/(km/liter) = $/km. The liters cancel.
Ok, so in the simpler number case, you would wind up with $2/3km, so you would travel 0.6(repeating)km/litre?

(I have a tendency to overthink things 😝)


\)
 

SweetDee93

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3
\(\displaystyle


Ok, so in the simpler number case, you would wind up with $2/3km, so you would travel 0.6(repeating)km/litre?

(I have a tendency to overthink things 😝)


\)
Bah I mean to say the cost per km would be 0.67/km ?

(Pardon my brain malfunction... Pregnant mum of a 4 year old over here trying to upgrade my math in my "spare" time! 😂😭)
 

Dr.Peterson

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Nov 12, 2017
Messages
4,156
That's right.

I would call it either 2/3 dollars/km, or just round it to the nearest cent as $0.67/km (not km/L). Writing the division as $2/3km, meaning ($2)/(3 km), looks as if you were saying this is the final answer, with the unit being $ times km.

I hope you didn't just do the division because I showed it, but also thought about the reason. But both ways (canceling unit fractions, and matching up amounts for one liter) are good ways to work it out.

Now, what do you get in your problem?
 

HallsofIvy

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Joined
Jan 27, 2012
Messages
5,046
Hi there, I feel really stupid :( word problems confuse me...

I am working on weighted averages and I am not sure how to translate part of my question into a formula to solve...

A motorist purchases gas as follows:
56 litres at 0.99/litre
64 litres at 1.065/litre
54 litres at 1.045/litre

I have already solved for the average number of litres of gas purchased, as well as the average cost per litre. The next question is if you average 8.75km per litre, what is the average cost of gasoline per km?

I'm not asking for anyone to solve it for me... I just want to know what I do with this information in order to solve it... Thanks!
You have already calculated the average cost per litre ($/Litre), and now you know the motorist averages 8.75 km/litre. You want "$/km". Dividing "$/Litre" by "km/Litre" cancels the "Litre" and leaves "$/km".
 
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