Question 1204176: The sum of the digits of a two-digit number is 14. The tens digit is the square of a number which is 2 less than the units digit. Find the two-digit number.
Found 3 solutions by mananth, greenestamps, ikleyn:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! The sum of the digits of a two-digit number is 14. The tens digit is the square of a number which is 2 less than the units digit. Find the two-digit number.
Let the digits in tens place be x
and the digit in units place be y
x+y=14............................................(1)
The tens digit is the square of a number which is 2 less than the units digit.
y= (x-2)^2.........................................(2)
substitute y in (1)
x+(x-2)^2= 14
x+x^2-4x+4=14
x^2-3x-10=0
factorize
x^2-5x+2x-10=0
x(x-5)+2(x-5)=0
(x-2)(x-5)=0
x=2 or x=5
x cannot be equal to 2
so x=5
y=9
The number = 59
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
In the response from the other tutor, she mixed up her variables, ending with an answer that doesn't satisfy the given conditions.
Her process is fine; you can turn her solution into a valid and correct solution by keeping the variables straight.
While undoubtedly a formal algebraic solution was wanted, the problem is solved quickly and easily using logical reasoning:
The sum of the two digits is 14, so the tens digit can only be 5, 6, 7, 8, or 9.
Since the tens digit is a perfect square, it must be 9.
That makes the units digit 14-9 = 5.
ANSWER: 95
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
In this problem, the sum of two digits 14 can be produced by the only one way: 14 = 9 (as the ten's digit, which is a square) + 5.
So, the all other info is simply not needed.
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