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Question 504509: a 2 digit number is equal to seven times the sum of its digits. if the digits are reversed, the new number formed is 36 less than the original number. what is the original number
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! a 2 digit number is equal to seven times the sum of its digits. if the digits are reversed, the new number formed is 36 less than the original number. what is the original number
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Let x = the original number
Let m = the tens place digit
Let n = the ones place digit
The number is formed by multiplying m by 10 and adding n:
10m + n = x
Given: x = 7 times the sum of its digits:
7(m + n) = x
Reversed, the new number is 36 less than x:
10n + m = x - 36
We have 3 equations in 3 unknowns. Solve using your favorite method.
You will get the answer n = 4, m = 8
So the original number is 84
Check:
7(8+4) = 7*12 = 84
84 - 48 = 36
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