Author 
Topic 

corchos68
New Member
USA
2 Posts 
Posted  10/10/2012 : 14:59:19

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?



royhaas
Moderator
USA
3059 Posts 
Posted  10/11/2012 : 08:22:20

Do you know what an arithmetic progression is? 


corchos68
New Member
USA
2 Posts 
Posted  10/11/2012 : 14:30:57

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.



royhaas
Moderator
USA
3059 Posts 
Posted  10/12/2012 : 08:05:00

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. 


Subhotosh Khan
Advanced Member
USA
9117 Posts 
Posted  11/20/2012 : 10:44:12

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 a_{n} = a_{n1}  0.5
or
a_{n} = 5  0.5 * (n1)



the_hill1962
Advanced Member
USA
1468 Posts 
Posted  11/26/2012 : 13:02:33

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: 50.5(111) = 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 50.5(1) = $4.50, not $5 as it wants. So, since "first" usually means n=1, you have to have 50.5(11) = $5
The 'simple explanation' for this problem would be to list the prices: 1st is 50.5(11) = 5 2nd is 50.5(21) = 4.5 3rd is 50.5(31) = 4 4th is 50.5(41) = 3.5 5th is 50.5(51) = 3 6th is 50.5(61) = 2.5 7th is 50.5(71) = 2 8th is 50.5(81) = 1.5 9th is 50.5(91) = 1 10th is 50.5(101) = 0.5 11th is 50.5(111) = 0




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