a two digit no.is 3more than 4 times the sum of its digit if 18 idded to the no.are reversed .find the no
By mental calculations:
Reverse number by adding 18 means the digits differ by 2, 13,24,35, etc.
13/31 does not work, 4*4+3=19
24/42 does not work either, 6*4+3=27
35/53 4*(5+3)+3=35 works.
The pair of numbers would be 35 and 53.
By mathematics.
Let x and y be the two digits
10x+y=10y+x+18
9(x-y)=18
(x-y)=2 (as stated above)
Note: x>y or y>x, we don't know yet.
10x+y=4(x+y)+3
3y=6x-3
2x=y+1, so y>x, or y=x+2
Substitute y=x+2 in 2x=y+1
2x=x+2+1
x=3
y=5
as before
The expression for a two-digit no is 10x y..nd d digits ar x and y..xo in ur first statement:d no is 3 mre dan 4 timez d digtz xo..et is10x y=3 4(x y)..d eqn becomez 2x-y=1
in d 2nd statemnt.i cudn't gt u wel bt wt ah gt z dat wen18 is added to the digit,d no z reversd:18 10x y=10y x..d eqn becomez 2=y-x...xo solve d 2 eqns simultaneously,x=3 nd y equals 5..xo d orignal no z 35
To find the two-digit number, we will break down the problem into steps.
Step 1: Represent the two-digit number as "10x + y," where x is the tens digit and y is the units digit.
Step 2: Translate the given information into an equation. The problem states that the number is three more than four times the sum of its digits: "10x + y = 4(x + y) + 3."
Step 3: Simplify the equation. Distribute 4 to both x and y:
10x + y = 4x + 4y + 3.
Step 4: Combine like terms:
10x - 4x + y - 4y = 3.
Simplify further:
6x - 3y = 3.
Step 5: The problem states that when 18 is added to the number, the digits are reversed. We can express this as:
10y + x + 18 = 10x + y.
Step 6: Simplify the equation:
10y - y + 18 = 10x - x.
Combine like terms:
9y + 18 = 9x.
Step 7: Now we have a system of equations:
6x - 3y = 3 (Equation 1)
9y + 18 = 9x (Equation 2)
Step 8: Solve the system of equations to find the values of x and y.
From Equation 2, we get:
9y = 9x - 18
y = x - 2
Substitute y = x - 2 into Equation 1:
6x - 3(x - 2) = 3
6x - 3x + 6 = 3
3x + 6 = 3
3x = -3
x = -1
Substitute the value of x into y = x - 2:
y = -1 - 2
y = -3
Therefore, the two-digit number is -13.