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December 20th, 2012, 05:36 PM   #1
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Fractional increase

Father reduced the quantity of food bought for the family by 10% when he found that the cost of living had increased by 15%. Thus the fractional increase in the family food bill now is what?

I don't know how those things relate to one another.


The quantity of food bought for the family is not given. In fact, I don't know how those things relate to one another.

Where and how do I start from?
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December 20th, 2012, 05:58 PM   #2
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Re: Fractional increase

Assuming a 10% decrease in the quantity of food purchased results in a 10% reduction in the cost of the food that Father buys and a 15% increase in the cost of living causes a 15% increase in the cost of the food that Father buys, we have:

New cost of food = Old cost of food * 0.9 * 1.15 = Old cost of food * 1.035,

so the increase in the food bill is 3.5%.
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December 20th, 2012, 09:46 PM   #3
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As a fraction, 7/200.
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December 21st, 2012, 04:09 PM   #4
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Re: Fractional increase

@greg1313,

Is this operating based on the principle in Economics that says that the lower the quantity demanded, the lower the cost and the higher the quantity demanded the higher the cost?

Which is the new cost of food? Which is the old cost of food?

How do you got 0.9 and 1.15 respectively?
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December 21st, 2012, 05:03 PM   #5
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Re: Fractional increase

"new cost of food" and "old cost of food" are variables. I assumed that a ten percent decrease in the amount of food purchased results in a ten percent reduction of the cost of the food: old cost of food * 0.9. (A ten percent reduction means that the old cost of food will be 90% of its previous cost). A similar idea applies for the 15% increase in the cost of living:

New cost of food = Old cost of food * 0.9 * 1.15 = Old cost of food * 1.035.

This is just arithmetic based on percentages and doesn't involve any economic theory that I know of.
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December 26th, 2012, 08:15 PM   #6
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Re: Fractional increase

@greg10

But in real life, can 10% reduction in quantity of food bought, cause a 10% decrease (reduction) in cost of the food bought?
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January 1st, 2013, 02:14 PM   #7
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Re: Fractional increase

That depends on how "10% reduction in quantity of food bought" is applied. If I buy 10% less eggs, 10% less fish, 10% less bread and so on, that is, 10% less of each item I usually buy, what happens?

Quote:
Originally Posted by Chikis
@greg10

But in real life, can 10% reduction in quantity of food bought, cause a 10% decrease (reduction) in cost of the food bought?
I'll say it's unlikely.
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January 2nd, 2013, 04:06 PM   #8
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Re: Fractional increase

I thought that new cost of food = new price of food * the quantity of new food

Similary, old cost of food = old price of food * the quantity of old food

I understand that you got the 0.9% and 1.15% when you evaluated the percentage decrease (in the quantity of food bought) and percentage increase (in the price of food).

So how come is that new cost of food = old cost of food * 0.9*1.15?
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January 2nd, 2013, 04:42 PM   #9
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Re: Fractional increase

Because we're reducing the cost by 10%, then increasing the cost by 15%.
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January 3rd, 2013, 09:32 AM   #10
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Re: Fractional increase

What if we decide to do the opposite?
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