Question
The average of first three numbers of a set of six
numbers is 60 .The average of the second, third and fourth numbers is 20 and the average of the third, fourth and fifth numbers is 30. The average of last three numbers is 40. What is the average of first three and last three numbers of the set?Solution
We are given four conditions involving averages of groups of three numbers from a set of six numbers a,b,c,d,e,f:
We add these equations to get = a+2b+3c+3d+2e+f = 450 Then, using the known sums a+b+c =180 and d+e+f=120, we substitute them into the equation: 180+120+(b+2c+2d+e) = 450 This simplifies to:b+2c+2d+e=150 The total sum of all six numbers is 180+120 = 300. Therefore, the average of the first three and last three numbers is: 300/6 = 50
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