SOLUTION: the tens of a two digit number is twice the units digit. if the number is multiplied by the sum of its digits the product is 63. whats the number?

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Question 618972: the tens of a two digit number is twice the units digit. if the number is multiplied by the sum of its digits the product is 63. whats the number?
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
The actual number is +10t+%2B+u+
given:
(1) +t+=+2u+
(2) +%28+t+%2B+u+%29%2A%28+10t+%2B+u+%29+=+63+
-------------------------
Substitute (1) into (2)
(2) +%28+2u+%2B+u+%29%2A%28+10%2A2u+%2B+u+%29+=+63+
(2) +3u+%2A+21u+=+63+
(2) +21u+=+21+
(2) +u+=+1+
and
(1) +t+=+2u+
(1) +t+=+2+
The number is 21
check:
(2) +%28+t+%2B+u+%29%2A%28+10t+%2B+u+%29+=+63+
(2) +%28+2+%2B+1+%29%2A%28+10%2A2+%2B+1+%29+=+63+
(2) +3%2A21+=+63+
(2) +63+=+63+
OK