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?

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the_hill1962

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: 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

Subhotosh Khan

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_{n-1} - 0.5

or

a_{n} = 5 - 0.5 * (n-1)

royhaas

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.

corchos68

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

Posted - 10/11/2012 : 08:22:20 Do you know what an arithmetic progression is?