Separate 178 into two parts such that the first part is 8 less than twice the second part. Explain!
x + 2x-8 = 178
To solve this problem, we can use algebraic equations. Let's assume the second part of the number is represented by "x".
According to the given information, the first part is 8 less than twice the second part. In equation form, this can be written as:
First part = 2 * second part - 8
Now, we can substitute the value of the second part, which we represented as "x", into the equation:
First part = 2x - 8
We also know that the sum of the two parts equals 178. In equation form, this is:
First part + second part = 178
Now we can substitute the expression for the first part, 2x - 8, into this equation:
2x - 8 + x = 178
Now it's a simple matter of solving for "x" to find the second part of the number:
3x - 8 = 178
3x = 186
x = 62
So, the second part of the number is 62. Now we can find the first part by substituting this value back into the equation for the first part:
First part = 2x - 8 = 2(62) - 8 = 116
Therefore, the two parts of the number 178 are 116 and 62, where the first part is 8 less than twice the second part.