SOLUTION: the tens didigit of a certain two digit number is twice the units digit. if the numberis multiplied by the sum of it's digit, the product is 63. find the numebr

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Question 915237: the tens didigit of a certain two digit number is twice the units digit. if the numberis multiplied by the sum of it's digit, the product is 63. find the numebr
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+=+2u+
---------------
The number is:
+10t+%2B+u+
(2) +%28+10t+%2B+u+%29%2A%28+t+%2B+u+%29+=+63+
(2) +10t%5E2+%2B+u%2At++%2B+10u%2At+%2B+u%5E2++=+63+
(2) +10t%5E2+%2B+11u%2At+%2B+u%5E2++=+63+
---------------
Substitute (1) into (2)
(2) +10%2A%282u%29%5E2+%2B+11u%2A2u+%2B+u%5E2++=+63+
(2) +40u%5E2+%2B+22u%5E2+%2B+u%5E2+=+63+
(2) +63u%5E2+=+63+
(2) +u+=+1+
and
(1) +t+=+2%2A1+
(1) +t+=+2+
The number is 21
------------------
check:
(2) +%28+10t+%2B+u+%29%2A%28+t+%2B+u+%29+=+63+
(2) +21%2A%28+2%2B+1+%29+=+63+
(2) +21%2A3+=+63+
(2) +63+=+63+
OK