SOLUTION: The sum of three numbers is 26. The third number is twice the second, and is also 1 less than 3 times the first. What are the three numbers?

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Question 1070327: The sum of three numbers is 26. The third number is twice the second, and is also 1
less than 3 times the first. What are the three numbers?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x%2By%2Bz=26%2Cz=2y%2Cz=3x-1%29

system%28y=z%2F2%2Cand%2Cx=%28z%2B1%29%2F3%29
Substitute into the first equation.

%28z%2B1%29%2F3%2Bz%2F2%2Bz=26-----start by solving for z.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
The sum of three numbers is 26. The third number is twice the second, and is also 1
less than 3 times the first. What are the three numbers?
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The solution by "josgarithmetic" was wrong.


Below is my corrected solution. 

x + y + z = 26,   (1)
z = 2y,           (2)
z = 3x - 1.       (3)

From (2),  y = z%2F2.

From (3),  x = %28z%2B1%29%2F3.

Substitute it into (1). You will get

%28z%2B1%29%2F3+%2B+z%2F2+%2B+z = 26.

Write it with the common denominator, which is 6. You will get

%28%282z%2B2%29+%2B+3z+%2B+6z%29%2F6 = 26,   or

11z + 2 = 156  --->  11z = 156 - 2  --->  z = 154%2F11 = 14.

Then y = 7  and  x = 5.

Answer.  x = 5,  y = 7,  z = 14.