SOLUTION: In a number represented by a two-digit numeral, the sum of the digits is equal to one-seventh of the number. Find all the numbers greater than 50 satisfying these conditions. I've

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Question 766358: In a number represented by a two-digit numeral, the sum of the digits is equal to one-seventh of the number. Find all the numbers greater than 50 satisfying these conditions.
I've tried to solve it but can't get past a + b = 1/7ab?. Please I would like to know how to solve it.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Maybe expressing the equation correctly would have kept you better oriented.
Your number would be like 10a%2Bb.
The description would give you a%2Bb=%281%2F7%29%2810a%2Bb%29.

7a%2B7b=10a%2Bb
.
6b=3a
highlight%282b=a%29 the way to relate the digits.
a is for the tens place, and b is for the ones place.

You want all numbers 10a+b greater than 50 that fit?
So 'a' must be half of 'b'.
(5)(?)-----This does not work.
(6)(3) -----This works, so number is 63.
(7)(?) ----not this .
(8)(4)------another fit, so number is 84.
(9)(?)----Not any possible integer single digit.

SUMMARY: The possible numbers are 63 and 84.