SOLUTION: The Sum of Two Digits Number is same as its product. find the Number? Ans is 22 but I dont know how it comes.

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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): You can put this solution on YOUR website!
the two digit number.

-----? Product with WHAT? With itself?




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?


----
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.
Answer by MathTherapy(10858)   (Show Source): 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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