SOLUTION: The sum of three numbers is 34. The largest number is five more than three times the smallest number. The middle number is four less than the largest number. What are the three n

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Question 1128900: The sum of three numbers is 34. The largest number is five more than three times
the smallest number. The middle number is four less than the largest number. What
are the three numbers?
Found 2 solutions by Edwin McCravy, josgarithmetic:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of three numbers is 34. The largest number is five more than three times
the smallest number. The middle number is four less than the largest number. What are the three numbers?
S = Smallest number
M = Middle number
L = Largest number

The sum of three numbers is 34.
A.     S + M + L = 34

The largest number is five more than three times
the smallest number.
B.     L = 3S + 5

The middle number is four less than the largest number. 
C.     M = L - 4

Use B to substitute (3S + 5) for L in C:

C.     M = L - 4
       M = (3S + 5) - 4
       M = 3S + 5 - 4
D.     M = 3S + 1

Use D to substitute (3S + 1) for M and 
use B to substitute (3S + 5) for L in A

A.     S + M + L = 34
       S + (3S + 1) + (3S + 5) = 34
       S + 3S + 1 + 3S + 5 = 34
       7S + 6 = 34
       7S = 28
E.     S = 4

Use E to substitute (4) for S in D 

D.     M = 3S + 1
       M = 3(4) + 1
       M = 12 + 1
F.     M = 13

Use F to substitute (13) for M and
use E to substitute (4) for S in A

A.     S + M + L = 34
       4 + 13 + L = 34
       17 + L = 34
       L = 17  

Edwin

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Numbers         Expressions
smallest          x
middle           3x+5-4
largest          3x+5
TOTAL            34

highlight%28x%2B%283x%2B5-4%29%2B%283x%2B5%29=34%29
-
x%2B3x%2B1%2B3x%2B5=34
7x%2B6=34
7x=28
highlight%28x=4%29 


Numbers         Expressions  VALUES
smallest          x            highlight%284%29
middle           3x+5-4       highlight%2813%29
largest          3x+5         highlight%2817%29
TOTAL            34           34