Certainly! Let's tackle each part of the problem step-by-step.
### Part 1: Finding the number
Problem: One-fourth of a number is 6. Find the number.
Solution:
1. Let's denote the unknown number by [tex]\( x \)[/tex].
2. According to the problem, one-fourth of this number is given to be 6. Mathematically, this can be written as:
[tex]\[
\frac{1}{4} x = 6
\][/tex]
3. To find the value of [tex]\( x \)[/tex], we need to get rid of the fraction by multiplying both sides of the equation by 4:
[tex]\[
x = 6 \times 4
\][/tex]
4. Simplifying the right-hand side, we get:
[tex]\[
x = 24
\][/tex]
Thus, the number is 24.
### Part 2: Finding three consecutive numbers whose sum is given
Since the sum is not provided in your question, I will provide a general solution for any given sum [tex]\( S \)[/tex].
Problem: Find three consecutive numbers whose sum is [tex]\( S \)[/tex].
Solution:
1. Let the three consecutive numbers be [tex]\( n \)[/tex], [tex]\( n+1 \)[/tex], and [tex]\( n+2 \)[/tex].
2. According to the problem, the sum of these three numbers is given by:
[tex]\[
n + (n+1) + (n+2) = S
\][/tex]
3. Simplifying the left-hand side, we get:
[tex]\[
3n + 3 = S
\][/tex]
4. To solve for [tex]\( n \)[/tex], first isolate [tex]\( 3n \)[/tex] by subtracting 3 from both sides:
[tex]\[
3n = S - 3
\][/tex]
5. Finally, divide both sides by 3:
[tex]\[
n = \frac{S - 3}{3}
\][/tex]
Hence, the three consecutive numbers are:
1. [tex]\( n = \frac{S - 3}{3} \)[/tex]
2. [tex]\( n+1 = \frac{S - 3}{3} + 1 \)[/tex]
3. [tex]\( n+2 = \frac{S - 3}{3} + 2 \)[/tex]
This gives you the three consecutive numbers for any given sum [tex]\( S \)[/tex]. If you provide a specific sum, I can calculate the specific consecutive numbers for that sum.
