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
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