Question 200815
The arithmetic mean of 6 numbers is 17. 
If two numbers are added, the new set of numbers will have an arithmetic mean of 19. 
What are the two numbers if their difference is 4?
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Mean is the same as average.
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Let the two number be x & y
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Write an equation for each statement:
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"If two numbers are added, the new set of numbers will have an arithmetic mean of 19." 

{{{(6(17) + x + y)/8}}} = 19
{{{(102 + x + y)/8}}} = 19
Multiply both side by 8, results
x + y + 102 = 152
x + y = 152 - 102
x + y = 50
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"What are the two numbers if their difference is 4?
x - y = 4
x = (y+4)
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Substitute (y+4) for x in the 1st equation, find y
(y + 4) + y = 50
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2y = 50 - 4
y = {{{46/2}}}
y = 23 is one number
then
x - 23 = 4
x = 27 is the other number
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Check solution
{{{(102 + 27 + 23)/8}}} =
{{{152/8}}} = 19
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Did this make sense to you? Any questions