SOLUTION: The first number is two more than twice a second number. If their product is 24, what are the numbers

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Question 1146488: The first number is two more than twice a second number. If their product is 24, what are the numbers
Found 4 solutions by josgarithmetic, greenestamps, MathTherapy, ikleyn:
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
first number            2x+2
second number            x
product                 x(2x+2)=24

Are you thinking, 3 & 8 ?
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


If a formal algebraic solution is not needed, by far the fastest path to an answer is informal guess-and-check.

If one number is exactly 2 more than twice the other, and their product is a whole number, then the two numbers have to be whole numbers. So look for two whole numbers whose product is 24 that satisfy the condition that one is 2 more than twice the other:

1 and 24? no....
2 and 12? no....
3 and 8? YES!

Done....
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
The first number is two more than twice a second number. If their product is 24, what are the numbers
Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.
Let x be the second number.


Then the first number is (2x+2).


The condition says


    x*(2x+2) = 24.


Simplify and solve for x


    x*(x+1) = 12.


The two solutions for x are obvious:  x= 3  and  x= -4.


It gives two pairs of the numbers, the problem asks for:


    one pair is        (2*3+2,3)     = (8,3);


    the other pair is  (2*(-4)+2,-4) = (-6,-4).

Solved.

-----------------

The lesson to learn from my post is THIS : 

    When you "guess", be careful :  guessing does not guarantee that you get all solutions.


    Algebra guarantees (when it works . . . )


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