Question 1070327
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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.


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

From (2),  y = {{{z/2}}}.

From (3),  x = {{{(z+1)/3}}}.

Substitute it into (1). You will get

{{{(z+1)/3 + z/2 + z}}} = 26.

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

{{{((2z+2) + 3z + 6z)/6}}} = 26,   or

11z + 2 = 156  --->  11z = 156 - 2  --->  z = {{{154/11}}} = 14.

Then y = 7  and  x = 5.

<U>Answer</U>.  x = 5,  y = 7,  z = 14.
</pre>