A certain number has 3 digits.The sum of 3 digits =36 multiplied by the 3digits number.What is the 3 digit number?
To find the three-digit number that satisfies the given conditions, let's break down the problem step by step.
Step 1: Assign variables
Let's assign variables to the hundreds, tens, and units digits of the three-digit number. We'll call them "h," "t," and "u," respectively.
Therefore, the three-digit number can be represented as "h * 100 + t * 10 + u."
Step 2: Write equations based on the given conditions
The sum of the three digits is equal to 36 multiplied by the three-digit number. We can write this condition using equations:
h + t + u = 36 --- Equation 1
(h * 100 + t * 10 + u) = 36 * (h * 100 + t * 10 + u) --- Equation 2
Step 3: Simplify the equations
Let's manipulate Equation 2 to simplify it:
h * 100 + t * 10 + u = 36 * (h * 100 + t * 10 + u)
h * 100 + t * 10 + u = 3600h + 360t + 36u
Step 4: Continue to simplify Equation 2
Rearrange the terms in Equation 2 to isolate the variables on one side and constant terms on the other side:
h * 100 - 3600h + t * 10 - 360t + u - 36u = 0
-3500h - 350t - 35u = 0
-100h - 10t - u = 0 --- Equation 3
Step 5: Solve the system of equations
Now we have two equations: Equation 1 and Equation 3. We can solve this system of equations to find the values of "h," "t," and "u."
Using any method of solving linear equations (e.g., substitution, elimination, etc.), we can find that the values of "h," "t," and "u" are 4, 8, and 24, respectively.
Step 6: Find the three-digit number
Now that we have the values of "h," "t," and "u," we can substitute them back into the equation for the three-digit number:
h * 100 + t * 10 + u = 4 * 100 + 8 * 10 + 24 = 408 + 80 + 24 = 512
Therefore, the three-digit number that satisfies the given conditions is 512.