Question

A number consists of 2 digits. The digit in ten's place exceeds the digit in unit's place by 4.The sum of digits is one-seventh of number. Find the number

Answer 1

Step-by-step explanation:

Establish the variables

x = tens place

y = ones place

...

Given

x = y+3

x+y = (10x+y)

...

Substitute x into the equation

y+3 + y = (10(y+3) + y)

...

Distribute the 10

2y + 3 = (10y + 30 + y)

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Combine like terms

2y + 3 = (11y + 30)

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Multiply both sides by 7 to be rid of the fraction

14y + 21 = 11y + 30

Isolate y

14y - 11y = 30 - 21

3y = 9

y =9

...

x = y+3 = 3+3

x=6

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Then number is 63

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Check 

Answer 2

Establish the variables
x = tens place
y = ones place
...
Given
x = y+3
x+y = (10x+y)
...
Substitute x into the equation
y+3 + y = (10(y+3) + y)

...
Distribute the 10
2y + 3 = (10y + 30 + y)
...
Combine like terms
2y + 3 = (11y + 30)
...
Multiply both sides by 7 to be rid of the fraction
14y + 21 = 11y + 30
Isolate y
14y - 11y = 30 - 21
3y = 9
y =9

...
x = y+3 = 3+3
x=6
...
Then number is 63