SOLUTION: the sum of the square of three digit number is 26.if the difference between tens' and hundreds' digit is equal to the units' digit.find the number if the sum of the 3 digit no. is

Question 301273: the sum of the square of three digit number is 26.if the difference between tens' and hundreds' digit is equal to the units' digit.find the number if the sum of the 3 digit no. is equal to 8.
help me to answer please...
thanks..jessa!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let the 3 digit number = 100x + 10y + z
:
"the sum of the square of a three digit number is 26."
Proceed with the next two statements
:
"the difference between tens' and hundreds' digit is equal to the units' digit."
y - x = z
-x + y - z = 0
:
find the number if the sum of the 3 digit no. is equal to 8.
x + y + z = 8
:
Add the two equations, find y
x + y + z = 8
-x +y - z = 0
------------------addition eliminates x and z, find y
2y = 8
y = 4
:
therefore x + z = 4
not many choices, only 4 if you include 0
341 or 143 or 242 or 440
;
Square these numbers and see if the digit adds up to 26
341^2 = 116281,
143^2 = 20449,
440^2 = 193600
All the above each add up to 19
242^2 = 58564 adds up 28,
None add up to 26 ???
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