SOLUTION: 1. Twice a number decreased by 39 is five times the sum of the number and two times the number .

Question 513949: 1. Twice a number decreased by 39 is five times the sum of the number and two times the number .
Answer by drcole(72) (Show Source): You can put this solution on YOUR website!
We need to write this problem out algebraically. Let x be the number. Then twice that number is 2x, and twice the number decreased by 39 can be written as:

The sum of the number and two times the number would be

The problem states that twice a number decreased by 39 equals five time the sum of the number and two times the number. We can therefore write this equation algebraically as:

Now we simplify our equation and solve for x:
(combine like terms)
(simplify the right hand side by multiplying)
(subtract 2x from both sides)
(divide both sides by 13)
So x = -3. Let's check this: twice of -3 is -6, so twice of 3 decreased by 39 equals -6 - 39 = -45. The sum of -3 and twice of -3 is -3 + (-6) = -9, and five times that is -45. So the two sides match, and x = -3 is our solution.
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