SOLUTION: Question: A number consists of two digits. The no. is 3 less than seven times the sum of their digits. If the order of the digit is changed then the new no. is 18 less than the ori

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Question 188634: Question: A number consists of two digits. The no. is 3 less than seven times the sum of their digits. If the order of the digit is changed then the new no. is 18 less than the original no. Find the no.?
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
ab can be written as 10a+b.....ba can be written as 10b+a
:
10a+b=7(a+b)-3.........eq 1--->10a+b=7a+7b-3--->3a-6b=-3
10b+a=10a+b-18.........eq 2------------------->-9a+9b=-18
:
3a-6b=-3......revised eq 1
-9a+9b=-18.....revised eq 2
:
multiply eq 1 by 3 and add the two equations together. a terms will be eliminated and we are left with -18b+9b=-9-18
:
-9b=-27
:
b=3
:
plug b's value into any equation ...I chose revised eq 1
3a-6(3)=-3
:
3a=15
:
a=5
:
original number is 53