A number of two digit is such that four times the unit digit is five greater than trice the tense digit.when the digit are reserved,the number is increased by nine find the number.
To solve this problem, let's break it down step by step.
Let's assume the tens digit is 'x' and the units digit is 'y'.
From the given information, we know that the number is a two-digit number, so we can write it as 10x + y.
According to the first condition, four times the unit digit (4y) is five greater than three times the tens digit (3x). We can write this as:
4y = 3x + 5 (Equation 1)
The second condition states that when the digits are reversed, the number is increased by nine. This means that the new number is 10y + x, and it is nine more than the original number:
10y + x = 10x + y + 9
Simplifying this equation gives:
10y - y = 10x - x + 9
9y = 9x + 9
y = x + 1 (Equation 2)
Now we have a system of equations (Equations 1 and 2) with two variables, x and y. We can substitute Equation 2 into Equation 1 to eliminate one variable and solve for the other variable.
4y = 3x + 5
4(x + 1) = 3x + 5
4x + 4 = 3x + 5
x = 1
Substituting the value of x back into Equation 2:
y = x + 1
y = 1 + 1
y = 2
Therefore, the number is 10x + y = 10(1) + 2 = 12.
If your question means:
A two digits number is such that four times the unit digit is five times greater than the tens digit. When the digits are reversed, the number is increased by nine. Find the number?
then
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