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If the arithmetic mean (average) of 10 consecutive integers is 15½, arranged in increasing order, what is the mean of the first five?

By .. on Wednesday, December 25, 2002 - 11:35 pm: Edit

that's really easy. i will solved it in 1 minute...

By .. on Wednesday, December 25, 2002 - 11:37 pm: Edit

13

By me on Wednesday, December 25, 2002 - 11:40 pm: Edit

let the smallest integer be "x".. therefore, if you set up the equation,
[ x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)+(x+6)+(x+7)+(x+8)+(x+9) ] / 10 = 15.5
multiply each side by 10.. so the sum would equal 155... then simplyfy the equation so it becomes:
10x + 45 = 155
subtract 45 from each side.. 10x = 110.. therefore x is 11.. but the question asks for the mean of the first five.. so it is actually asking for the mean of [11, 12, 13, 14, 15].. so the mean would be 13
therefore, the final answer is 13..