SOLUTION: a number is composed of two digits the difference of whose squares is 20. if the digits are interchanged the resulting number is 18 less than the original number. find the number.

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Question 1012476: a number is composed of two digits the difference of whose squares is 20. if the digits are interchanged the resulting number is 18 less than the original number. find the number.
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the tens digit
Let +u+ = the units digit
-------------------------
(1) +t%5E2+-+u%5E2+=+20+
(2) +10u+%2B+t+=+10t+%2B+u+-+18+
---------------------------
(2) +9t+-+9u+=+18+
(2) +t+-+u+=+2+
(2) +t+=+u+%2B+2+
Substitute (2) into (1)
(1) %28+u+%2B+2+%29%5E2+-+u%5E2+=+20+
(1) +u%5E2+%2B+4u+%2B+4+-+u%5E2+=+20+
(1) +4u+=+16+
(1) +u+=+4+
and
(2) +t+=+u+%2B+2+
(2) +t+=+4+%2B+2+
(2) +t+=+6+
The tens digit is 6
The units digit is 4
The number is 64
-----------------
check:
(1) +t%5E2+-+u%5E2+=+20+
(1) +6%5E2+-+4%5E2+=+20+
(1) +36++-+16+=+20+
(1) +20+=+20+
OK

Answer by ikleyn(52803) About Me  (Show Source):