Question 970051: The Sum of Two Digits Number is same as its product. find the Number?
Ans is 22 but I dont know how it comes. Found 2 solutions by josgarithmetic, MathTherapy:Answer by josgarithmetic(39838) (Show Source):
Not sure that this is even within College Algebra, seeing a term, and only one equation but two variables. You expect only t and u are digits. One way although lengthy, is solve for t and test all values of u from the digits 0 through 9. With each of those u values, finish solving for t, which also must be a digit.
Just checking your expected "22",
10*2+2+10*2+2=22*22
20+2+20+2=2*2*11*11
44=4*121
NO GOOD!
Better, what is the exact problem description and question, word-for-word?
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New Description: Sum of the digits is equal to the product of the digits, for an unknown two digit number.
t and u for the Tens place and the Ones place.
Just one equation but two unknown variables.
You know that u and t must be from the set of digits. You can start with u at 0 and cycle through to u at 9 and solve t for each case until something works (meaning t is found as a digit). You first find that u=0 gives you nothing.
u________________t
0________________0
1______________meaningless by undefined
2_______________2
3_______________
4_______________
5_______________
Following the pattern you see the rest will not work.
Only one of those combinations gave a digit for t.
That is the number 22.
You can put this solution on YOUR website! The Sum of Two Digits Number is same as its product. find the Number?
Ans is 22 but I dont know how it comes.
Let number’s tens and units digits be T and U, respectively
Then: T + U = TU
TU – T = U
T(U – 1) = U
In order for T to be an integer > 0 in the above equation, U – 1 MUST BE 1.
We then get: U - 1 = 1
U = 1 + 1, or
We then get: , or , or
Therefore, T = 2, and U = 2
Number:
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