Question

A number of two digit is such that four times the unit digit is 5 greaterthan twice the ten digit. When the digits are reversed the number is increase by 9. Find the number

Answer 1

a = the tens digit

b = the unit digit

Your number is:

x = 10 a + b

Four times the unit digit is five time greater than twice the tens digit means:

4 b = 5 a

When the digit are reserved new number is 10 b + a

When the digit are reserved, the number is increased by nine means:

10 b + a = x + 9

Replace x with 10 a + b in this equation

10 b + a = 10 a + b + 9

Subtract b to both sides

9 b + a = 10 a + 9

Subtract a to both sides

9 b = 9 a + 9

Divide both sides by 9

b = a + 1

Now you must solve system:

4 b = 5 a

b = a + 1
_______

The solution is a = 4 , b = 5

x = 10 a + b

x = 10 ∙ 4 + 5

x = 40 + 5

x = 45