SOLUTION: When three numbers are added together, the result is 665. The largest number is one-third more than the sum of the other two numbers. What is the value of the largest number? A)

Algebra ->  Equations -> SOLUTION: When three numbers are added together, the result is 665. The largest number is one-third more than the sum of the other two numbers. What is the value of the largest number? A)       Log On


   

Question 1045513: When three numbers are added together, the result is 665. The largest number is one-third more than the sum of the other two numbers. What is the value of the largest number?
A) 95
B) 245
C) 350
D) 380
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
x%3Cy%3Cz
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system%28x%2By%2Bz=665%2Cz=%281%2F3%29%2B%28x%2By%29%29, three unknown variables and two equations only.

The sum of x%2By is part of BOTH equations.

x%2By=z-1%2F3
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%28x%2By%29%2Bz=665
%28z-1%2F3%29%2Bz=665
2z-1%2F3=665
2z=665%2B1%2F3
6z=3%2A665%2B1
6z=1996
highlight%28z=332%262%2F3%29, which does not match any of the choices.

Second sentence of the problem description is possibly ambiguous; you can examine the other interpretation.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

When three numbers are added together, the result is 665. The largest number is one-third more than the sum of the other two numbers. What is the value of the largest number?
A) 95
B) 245
C) 350
D) 380
Let smallest, middle, and largest numbers be S, M, and L, respectively

Then: S + M + L = 665______S + M = 665 – L ------ eq (i)			

Also, L+=+S+%2B+M+%2B+%281%2F3%29+%2A+%28S+%2B+M%29_____L+=+S+%2B+M+%2B+%28S+%2B+M%29%2F3 -------- eq (ii)			

L+=+665+-+L+%2B+%28665+-+L%29%2F3 ------- Substituting 665 – L for S + M in eq (ii)			

3L = 1,995 - 3L + 665 – L ------ Multiplying by LCD, 3			

3L = 2,660 – 4L 

3L + 4L = 2,660			

7L = 2,660			

L, or larger number =