Nine numbers are written in increasing order. The average of the nine numbers is the middle number, the average of the five largest values is 68, and the average of the five smallest values is 44. What is the sum of the nine numbers?
Since you already have the average of 5 largest values, or 68, and the average of the 5 smallest values, or 44, then all have to do is to take the average of the two averages! That is [68 +44] / 2 * 9 =504 - the sum of the 9 numbers in the sequence.
(x1 + x2 + x3 + x4 + x5 +x6+x7+x8+x9)/9 = x5 given
x1+ x2+ x3+ x4+ x5 + x6 + x7 + x8 + x9 = 9 x5 (we'll use this shortly)
(x1 + x2 + x3 + x4 + x5)/5 = 44 5x44 = 220 = (x1+x2+x3+x4+x5)
(x5 + x6 + x7 + x8+ x9)/5 = 68 340 = (x5+x6+x7+x8+x9) Add these together
x1+ x2+ x3+ x4+ 2x5 + x6 + x7 + x8 + x9 = 560 subtract x5 from both sides (use the red definition above for x5)
x1+ x2+ x3+ x4+ 2x5 + x6 + x7 + x8 + x9 - 9x5
x5 = 560 - 9x5
10x5 = 560 x5 = 56
9 * x5 = 9 x 56 = 504 total (as Guest found (easier) above!)