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 Basic Math and Pre-Algebra
 Expression for sequential decrease
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corchos68
New Member

USA
2 Posts

Posted - 10/10/2012 :  14:59:19  Show Profile  Reply with Quote
A vendor at the fair sells an item for $5. Every item after that is less 0.50 cents. How many items must you buy before you get a free one? First one is $5, 2nd is $4.50, 3rd is $4 and so on until the eleventh item is free.
Is there a way to write this as an algebra expression?
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royhaas
Moderator

USA
3059 Posts

Posted - 10/11/2012 :  08:22:20  Show Profile  Reply with Quote
Do you know what an arithmetic progression is?
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corchos68
New Member

USA
2 Posts

Posted - 10/11/2012 :  14:30:57  Show Profile  Reply with Quote
quote:
Originally posted by royhaas

Do you know what an arithmetic progression is?



I don't. The homework asked if I could think of a different way to express my work - and I could not though I imagined there exists a simple or at least more elegant way than what I did.
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royhaas
Moderator

USA
3059 Posts

Posted - 10/12/2012 :  08:05:00  Show Profile  Reply with Quote
The clue lies in the fact that the difference between successive terms is constant. Perhaps conducting an Internet search for "arithmetic progression" or "arithmetic series" will help.
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Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 11/20/2012 :  10:44:12  Show Profile  Reply with Quote
quote:
Originally posted by corchos68

A vendor at the fair sells an item for $5. Every item after that is less 0.50 cents. How many items must you buy before you get a free one? First one is $5, 2nd is $4.50, 3rd is $4 and so on until the eleventh item is free.
Is there a way to write this as an algebra expression?




a = 5
an = an-1 - 0.5

or

an = 5 - 0.5 * (n-1)
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 11/26/2012 :  13:02:33  Show Profile  Reply with Quote
Looking at the title for this topic, the explanations are great.
However, since this is in the "basic math" section, here is an simple explanation:
5-0.5(11-1) = 0

A lot of students get confused as to why "1" is subtracted.
The easy way is to just refer to the original problem where it states "the FIRST one is $5"
Note that 5-0.5(1) = $4.50, not $5 as it wants.
So, since "first" usually means n=1, you have to have 5-0.5(1-1) = $5

The 'simple explanation' for this problem would be to list the prices:
1st is 5-0.5(1-1) = 5
2nd is 5-0.5(2-1) = 4.5
3rd is 5-0.5(3-1) = 4
4th is 5-0.5(4-1) = 3.5
5th is 5-0.5(5-1) = 3
6th is 5-0.5(6-1) = 2.5
7th is 5-0.5(7-1) = 2
8th is 5-0.5(8-1) = 1.5
9th is 5-0.5(9-1) = 1
10th is 5-0.5(10-1) = 0.5
11th is 5-0.5(11-1) = 0
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