SOLUTION: the sum of three numbers is 65. one number is five more than a second number. it is also twice the third. find the numbers

Question 820273: the sum of three numbers is 65. one number is five more than a second number. it is also twice the third. find the numbers
Answer by Alpha Maximus(4) (Show Source): You can put this solution on YOUR website!
Let the 3 numbers be 'a' , 'b' and 'c' respectively and let 'a' be the largest number. Thus, we have that:
a+b+c=65.......(1)
a=b+5...........(2)
a=2c.............(3)
Thus, we have that: b=a-5(from 2) and c=0.5a
Substituting the alternate values of b and c(in terms of a) respectively into (1), we have:
a+(a-5)+0.5a=65
a+a-5+0.5a=65
2.5a=70
a=70/2.5=28
Thus, b=a-5=28-5=23 and c=0.5a=0.5*28=14
Therefore the numbers are 28, 23 and 14. Taadaa! :D
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