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RATIO Porblem-complex help

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by coolgirl26 » Sun Apr 19, 2009 12:41 pm
barrel of juice there is 30 l

in barrel of beer there are 80 L

if price ratio between barrel of juice to barrel of beer is 3:4

what is price ratio beween one liter of juice to one liter of beer

answer is 2:1
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by DanaJ » Sun Apr 19, 2009 1:39 pm
Say j = price of barrel of juice
b = price of barrel of beer.

We're told that j:b = 3:4. This means that j/b = 3/4 or that j = 3b/4.

Now, you've got 30l in a barrel of juice, so the price of one liter will be j/30.
Similarly, you have 80l in a barrel of beer, so the price of one liter will be b/80.

Use the fact that j = 3b/4 to conclude that the price of one liter of juice will be 3b/4 * 1/30 = b/40.

So you have that:
- one liter of beer is worth b/80
- one liter of juice is worth b/40
It's really pretty obvious that the second one is two times the first, so the ratio you're looking for is indeed 2:1.
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Re: RATIO Porblem-complex help

by Musiq » Sun Apr 19, 2009 2:01 pm
coolgirl26 wrote:barrel of juice there is 30 l

in barrel of beer there are 80 L

if price ratio between barrel of juice to barrel of beer is 3:4

what is price ratio beween one liter of juice to one liter of beer

answer is 2:1
Total Cost of Juice = 30*J -------- Eqn. 1
Total Cost of Beer = 80*B -------- Eqn. 2

Where J and B are the per liter prices of Juice and Beer respectively.

Always set up what it is that the question is asking of us first. In this case, the ultimate question is to find the value of J / B.

So, divide equation 1 by Equation 2:

(Total Cost of Juice) / (Total Cost of Beer) = (30*J) / (80*B)

Or,
3 /4 = 3/8 * (J/B)

Or,
J / B = 2:1
For love, not money.
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