The price of oil recently went from $7.80 to $10.40 per case of 12 quarts. Find the ratio of the increase in price to the original price. (type a simplified fraction)

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- anonymous

- schrodinger

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- Haseeb96

per case means per quart ???
@dolloway97

- Ciarán95

I'm not sure about the "per case of 12 quarts" part of the question and what it means, but I assume that it's irrelevant in how to go about answering it. The main part appears to be:
"Find the ratio of the increase in price to the original price"
So, our ratio should be:
\[Increase In Price : Original Price \]
or
\[(Final Price - Original Price) : Original Price\]
which is
\[(10.40 - 7.80) : 7.80\]
\[= 2.40 : 7.80\]
That's our ratio set up. In general though, we usually like to express ratios in which one of our values is '1' and then we are able to more easily compare the quantity/magnitude of the other part of the ratio against it. The question also appears to ask for our ratio to contain a "simplified fraction" if I'm not mistaken, so I presume that's what we have to here as well.
So, to simplify 2.40 : 7.80, we need to convert one of the values to 1. We could do this by dividing across by either of the two values, to make life easier I'm just going to choose the smallest of the two, 2.40.
\[\frac{ 2.40 }{ 2.40 } : \frac{ 7.80 }{ 2.40 }\]
\[= 1 : \frac{ 7.80 }{ 2.40 }\]
We then need to simplify our fraction down. There's a few different ways of doing this, the easiest of which is to simply type the fraction into a scientific calculator to produce the simplified fraction.
If you're not allowed to use a calculator in the solution, then the best thing to do is to convert 7.80 and 2.40 to fractions by hand, substitute these for their decimal equivalents and the denominator above and below should cancel each other out. This will leave us with our simplified fraction overall as well!

- Ciarán95

@dolloway97
http://www.mathsisfun.com/converting-decimals-fractions.html

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- anonymous

idk how to

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