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

Algebra.Com
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(52931)   (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.





 

RELATED QUESTIONS


The units digit of a two-digit number is 2 less than the tens digit. The sum of the... (answered by JulietG)

The sum of the digits of a two digit number is 14. The difference between the tens digit... (answered by opeodu)

The sum of the digits of a two digit number is 14. The difference between the tens digit... (answered by josgarithmetic,MathTherapy)

The tens digit of a certain number is 7 less than the units digit. The sum of the squares  (answered by checkley77)

the difference between the tens digit and the unit digit of a two digit number is 3.... (answered by nerdybill)

The sum of the digits of a two digit number is 12. The tens digit is 2 less than the... (answered by rothauserc,addingup)

Translate into algebraic symbol: Sum of the digits of a two-digit number if the tens... (answered by ikleyn)

The difference between the digits of a two digit number is 1. The number itself us 1 more  (answered by josgarithmetic,MathTherapy,greenestamps)

The tens digit of a two-digit number is 2 less than twice the units digit. The number is... (answered by Nate,stanbon)