Question 1106289: The average of 10 numbers is 24. The average of first four numbers is 16*3/4 of the next three number is 22*1/3. If the eighth number be less than the ninth and tenth numbers by 11 and 8 respectively, then the tenth number is :
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The average of 10 numbers is 24.
Sum of 10 no. = 240
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The average of first four numbers is 16*3/4
Sum of 1st four no.: 4*16.75 = 67
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of the next three number is 22*1/3
sum of next three no.: 3 * 22.33 = 67
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let x, y, z = the 8th, 9th & 10th numbers
Then we can write an equation
67 + 67 + x + y + z = 240
x + y + x = 240 - 134
x + y + z = 106
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If the eighth number be less than the ninth and tenth numbers by 11 and 8 respectively,
x = y - 11
x = z - 8
x = x therefore
y - 11 = z - 8
y = z - 8 + 11
y = z + 3
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then the tenth number is :
in the equation x + y + z = 106, replace x and y
(z-8) + (z+3) + z = 106
3z - 5 = 106
3z = 111
z = 111/3
z = 37 is the 10th number
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