SOLUTION: Hi the tens digit of a two digit number is 2 less than the units digit. The difference between the squares of the digits is 32. What is the number. thanks

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Question 1137225: Hi
the tens digit of a two digit number is 2 less than the units digit. The difference between the squares of the digits is 32. What is the number.
thanks

Found 3 solutions by mananth, MathTherapy, ikleyn:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
the tens digit of a two digit number is 2 less than the units digit. The difference between the squares of the digits is 32. What is the number.
Let x be in the ten's place and y be in the units place

x=y-2
x-y =-2
Second condition
x^2-y^2 =32
(x+y)(x-y) =32
plug in (x-y)
(x+y)(-2) = 32
(x+y) = (32/-2)=-16
solve the two equations
x-y=-02
x+y=-16
Add the equations
2x=-18
x=-9
therefore y =-7

Number is -97

Answer by MathTherapy(10558)   (Show Source):
You can put this solution on YOUR website!

Hi
the tens digit of a two digit number is 2 less than the units digit. The difference between the squares of the digits is 32. What is the number.
thanks

Mananth's answer MAKES absolutely no sense.
Correct number:

Answer by ikleyn(52928)   (Show Source):
You can put this solution on YOUR website!
.

Let x = the ones digit and y = the tens digit. You are given x - y = 2 (1) x^2 - y^2 = 32 (2) Equation (2) is the same as (x-y)*(x+y) = 32. (3) In equation (3), replace the factor (x-y) by 2, based on the given (1). You will get 2*(x+y) = 32, x + y = 16. (4) We are at the finish line now . . . Add equations (1) and (2). You will get 2x = 16 + 2 = 18, hence, x = 18/2 = 9. Then y is 2 less than 9, i.e. 7. ANSWER. The two-digit number is 79. CHECK. 9^2 - 7^2 = 81 - 49 = 32. ! Correct !

Solved.