A positive two-digits number is such that the product of the digits is 24.When the digits are reversed,the number formed is greater than the original number by 18.Find the number
Let the digits be xy,x is the ones digit& y tens digit.Hence;
Xy=24---(i)
(X+10y)-(y+10x)=24---(ii)
(ii)
X+10y-y-10x
X-10x+10y-y
-9x+9y=18
9y-9x=18
Y-x=2--(ii)
but;xy=24
X=2+y
Y(2+y)=24
Y'2+2y-24=0
Product=-24
Sum=2
Numbers 6,-4
Since digits were(+)ignore the(-)sign
Product of digits xy;6×4=24,terrific
Therefore;
Original number=46
New number=64
let the unit digit be x
and the tens digit by y
then the original number is 10y + x
and the number reversed is 10x + y
10x + y - (10y + x) = 18
9x - 9y = 18
x - y = 2
but we also know that xy = 24
it should be obvious that the two number are 6 and 4.
Since reversing the numbers made the number bigger, the original must have been 46
check:
6x4 = 24 , that's good
original = 46
reversed = 64
64 - 46 = 18 , all is good!
. The product ofthe digits ina two digit number is 24. Four times the ten digit exceeds the unit digit by 10. Calculate the number
Oh, I love a good math puzzle! Let's solve this, shall we?
Let's assume the tens digit is 'a' and the ones digit is 'b'. We know that the product of the digits is 24, so we have the equation a * b = 24.
Now, we also know that when the digits are reversed, the new number is greater than the original number by 18. This means that the new number is equal to the original number plus 18, or (10*b + a) = (10*a + b) + 18.
Simplifying that equation gives us 9*b - 9*a = 18, which further simplifies to b - a = 2.
Now, we have two equations: a * b = 24 and b - a = 2. Let's solve them simultaneously.
Since b - a = 2, we can substitute b = a + 2 into the first equation, a * (a + 2) = 24. Expanding this equation gives us a^2 + 2a - 24 = 0.
Using the quadratic formula, we find that a = 4 or a = -6. Since we're looking for a positive two-digit number, we can discard the negative value.
So, a = 4. Substituting that back into the equation b - a = 2 gives us b - 4 = 2, which means b = 6.
Therefore, the number is 46.
To find the number, we need to find a two-digit number in which the product of its digits is 24, and when its digits are reversed, the new number is greater than the original number by 18.
Let's break it down step by step:
Step 1: Break down the problem.
We need to find a two-digit number where the product of the digits is 24. Let's call the number "10a + b" where "a" and "b" are the digits of the number. So, the problem can be represented as:
(a * b) = 24
Step 2: Set up the condition for the reversed number.
When we reverse the digits, the new number is greater than the original number by 18. This gives us the condition:
(10b + a) = (10a + b) + 18
Step 3: Solve the equations.
Using the equations, we can substitute the first equation into the second equation:
10b + a = 10a + b + 18
Simplifying the equation gives:
9b - 9a = 18
Dividing both sides by 9, we get:
b - a = 2
Step 4: Find the possible values of a and b.
Since a and b are digits, the possible values for a are 1, 2, 3, and 4. If we substitute these values into the equation b - a = 2, we find that the only possible value for b is 3.
Thus, a = 1 and b = 3.
Step 5: Find the number.
Now that we know the digits, let's substitute the values back into the original expression:
10a + b = 10(1) + 3 = 13
Therefore, the required number is 13.