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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):
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):
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.
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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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