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December 20th, 2012, 05:36 PM  #1 
Senior Member Joined: Jan 2012 Posts: 739 Thanks: 7  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? 
December 20th, 2012, 05:58 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,931 Thanks: 1126 Math Focus: Elementary mathematics and beyond  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%. 
December 20th, 2012, 09:46 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,471 Thanks: 2039 
As a fraction, 7/200.

December 21st, 2012, 04:09 PM  #4 
Senior Member Joined: Jan 2012 Posts: 739 Thanks: 7  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? 
December 21st, 2012, 05:03 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,931 Thanks: 1126 Math Focus: Elementary mathematics and beyond  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. 
December 26th, 2012, 08:15 PM  #6 
Senior Member Joined: Jan 2012 Posts: 739 Thanks: 7  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? 
January 1st, 2013, 02:14 PM  #7  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,931 Thanks: 1126 Math Focus: Elementary mathematics and beyond  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:
 
January 2nd, 2013, 04:06 PM  #8 
Senior Member Joined: Jan 2012 Posts: 739 Thanks: 7  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? 
January 2nd, 2013, 04:42 PM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,931 Thanks: 1126 Math Focus: Elementary mathematics and beyond  Re: Fractional increase
Because we're reducing the cost by 10%, then increasing the cost by 15%.

January 3rd, 2013, 09:32 AM  #10 
Senior Member Joined: Jan 2012 Posts: 739 Thanks: 7  Re: Fractional increase
What if we decide to do the opposite?


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