FIND the integer of
N=abcd....yz
let M=zabcd....y
if M=3N what was N?
please help me figure it out!
if m=3n, then zabcd=3abcd
which means z=3 which means N can equal anything....i think
To find the value of the integer N, given M = zabcd...y and M = 3N, we need to use a systematic approach.
Let's break down the problem step by step:
Step 1: Define the variables
Let's define the variables to represent each digit in the integers N and M:
N = abcd...yz
M = zabcd...y
Here, each letter represents a digit, and a, b, c, ..., y, z are specific digits.
Step 2: Determine the possible range of values for each digit
In this step, we need to determine the possible range of values for each digit in N. Since N and M are integers, each digit can have a value ranging from 0 to 9.
Step 3: Express N in terms of its digits
Next, we need to express N as a number, taking into account the positions of the digits.
N = a * 10^(n-1) + b * 10^(n-2) + c * 10^(n-3) + ... + y * 10 + z
Here, n represents the number of digits in N. Since we don't have the exact value of N, we will express it in general form.
Step 4: Express M in terms of its digits
Similarly, we need to express M as a number, taking into account the positions of the digits.
M = z * 10^(n-1) + a * 10^(n-2) + b * 10^(n-3) + ... + y * 10 + z
Step 5: Equation of M = 3N
We are given that M is equal to 3 times N. So we can write the equation as:
3N = M
Substituting the expressions for N and M from steps 3 and 4, we get:
3 * (a * 10^(n-1) + b * 10^(n-2) + c * 10^(n-3) + ... + y * 10 + z) = (z * 10^(n-1) + a * 10^(n-2) + b * 10^(n-3) + ... + y * 10 + z)
Step 6: Simplify the equation
Simplify the equation obtained in step 5 by expanding and rearranging terms:
3a * 10^(n-1) + 3b * 10^(n-2) + 3c * 10^(n-3) + ... + 3y * 10 + 3z = z * 10^(n-1) + a * 10^(n-2) + b * 10^(n-3) + ... + y * 10 + z
Step 7: Compare the coefficients of like terms
Compare the coefficients of like terms on both sides of the equation. In other words, compare the coefficients of each power of 10, from highest to lowest.
From the highest power of 10 (10^(n-1)) to the lowest power of 10 (10^0), compare the coefficients of a, b, c, ..., y, and z.
Step 8: Solve the equations
Set up and solve the resulting system of equations to find the values of the digits a, b, c, ..., y, and z. You can use substitution or elimination methods to solve the equations.
Once you find the values of the digits, you can substitute them back into the expression for N to find the value of N.