Question 1206161: A two digit number is such that it's product is 12 and when the digits are reversed the number exceeds the original number by 9, what is the original number?
Found 5 solutions by Alan3354, ikleyn, greenestamps, josgarithmetic, MathTherapy:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A two digit number is such that it's product is 12 and when the digits are reversed the number exceeds the original number by 9, what is the original number?
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Reversing the digits of a 2-digit # changes the value by 9 time the difference between the digits.
---> the difference between the digits = 1.
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U - T = 1
U = T + 1
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U*T = 12
T*(T+1) = 12
Solving gives the number is 34.
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it's = it is
Answer by ikleyn(52778)  (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Terrible English....
The 2-digit number does not have a product.
The statement should read "...is such that the product of its digits is 12..."
And note "its digits", not "it's digits".
Now a shortcut for this kind of problem, involving a 2-digit number and the 2-digit number formed by reversing the digits.
The difference between the two 2-digit numbers is 9 times the difference of the two digits.
In this problem, since the difference between the two 2-digit numbers is 9, the difference of the two digits is 1. So the two digits have a product of 12 and a difference of 1, making the two digits 3 and 4.
Finally, since the number with the digits reversed is larger, the number with the digits reversed is 43 and the original number is 34.
ANSWER: 34
Answer by josgarithmetic(39617)  (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
A two digit number is such that it's product is 12 and when the digits are reversed the number exceeds the original number by 9, what is the original number?
This should've read: "A two digit number is such that the product of its digits is 12." As such, the
numbers must be 2 and 6, or 3 and 4.
Let the tens and units digits be T and U, respectively
"when the digits are reversed the number exceeds the original number by 9."
This gives us: 10U + T = 10T + U + 9
- 9 + 10U + T = 10T + U
- 9 = 10T + U - 10U - T
- 9 = 9T - 9U
9(- 1) = 9(T - U)
- 1 = T - U____T = U - 1
With the tens digit being 1 less than the units digit, the 2 numbers CANNOT be 2 and 6, so
they MUST be 3 and 4 (TENS digit, or 3, being SMALLER than the UNITS digit, or 4).
DIGITS: 3 and 4, for the NUMBER 34
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