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mingshum
Senior Member

USA
29 Posts

 Posted - 02/25/2009 :  20:28:01 The average (arithmetic mean) weight of five students is 150.4 pounds. If no student weighs less than 130 pounds and if no two students' weights are within 5 pounds of each other, what is the most, in pounds that any one of the students can weigh?Answer is 202I know that the total weight is 752 and that's it! Please help.

the_hill1962

USA
1468 Posts

 Posted - 02/26/2009 :  08:14:49 Here is an overview of how to work with averages in non-routine problems:http://www.mathgoodies.com/lessons/vol8/advanced_mean.htmlBasically in your problem you want four out of the five to be as smallas possible (because you want one of the five to be as large (maximum)as possible.Your problem spells out what the smallest can be. It is 130. Yourproblem also spells out that no two are within 5 pounds of each other.How much bigger is the "next one" than 130 (remember you want to keepthem as small as possible). He/she can't be 131 (that would be "within5 pounts). Go exactly 5 pounds at 135. You see, 130 and 135 are NOT"within" 5 pounds of each other (you see, "within" would not includeexactly 5 pounds, "within" would include up to 134.9999999999999...pounds).Now, continuing, the next would be 140 pounds and 145 pounds.You have the average of 150.4 so add them up (denoting "M" to be thevariable for the largest person:(M+145+140+135+130)/5 = 150.4Solving for M gives 202

mingshum
Senior Member

USA
29 Posts

 Posted - 02/26/2009 :  11:23:28 Thank you to "the hill1962" for pointing out what "winthin 5 pounds"means! I was adding 6 pounds.
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