SOLUTION: The greatest of three numbers is 40 more than the smallest. The remaining number is 5less than 6 times the smallest number. Their sum is 3 times the middle number. Find the numbers

Question 346785: The greatest of three numbers is 40 more than the smallest. The remaining number is 5less than 6 times the smallest number. Their sum is 3 times the middle number. Find the numbers.
Found 2 solutions by rfer, ptaylor:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
x
x+40
6x-5
-----------
x+x+40+6x-5=3(6x-5)
8x+35=18x-15
-10x=-50
x=5
----------------------
proof
5+5+40+6*5-5=3(6*5-5)
75=75
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x= the smallest
Then x+40=the greatest number
(6 times the smallest=6x and 5 less than this is 6x-5)
so 6x-5=the remaining number
their sum is:
x+(x+40)+(6x-5) and this equals 3 times the middle number which is:3(6x-5)
so our equation to solve is:
x+(x+40)+(6x-5)=3(6x-5) get rid of parens:
x+x+40+6x-5=18x-15 simplify
8x+35=18x-15
subtract 18x and also 35 from each side
8x-18x+35-35=18x-18x-15-35 collect like terms
-10x=-50 divide each side by -10
x=5---smallest
x+40=5+40=45 greatest
6x-5=30-5=25 the middle number
CK
sum is three times the middle number:
45+5+25=3*25
75=75---ok
Greatest is 40 more than the smallest
45 is 40 more than 5---ok
The middle number:
5 less than 6 times the smallest:
6*5-5=25-----ok
Hope this helps--ptaylor
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