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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
3039 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 royhaasDo 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
3039 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

USA
9114 Posts

 Posted - 11/20/2012 :  10:44:12 quote:Originally posted by corchos68A 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 = 5an = an-1 - 0.5oran = 5 - 0.5 * (n-1)

the_hill1962

USA
1440 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:5-0.5(11-1) = 0A 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) = \$5The 'simple explanation' for this problem would be to list the prices:1st is 5-0.5(1-1) = 52nd is 5-0.5(2-1) = 4.53rd is 5-0.5(3-1) = 44th is 5-0.5(4-1) = 3.55th is 5-0.5(5-1) = 36th is 5-0.5(6-1) = 2.57th is 5-0.5(7-1) = 28th is 5-0.5(8-1) = 1.59th is 5-0.5(9-1) = 110th is 5-0.5(10-1) = 0.511th is 5-0.5(11-1) = 0
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