Sure, let's solve the problem of finding four consecutive natural numbers whose sum is 98.
Let's represent the four consecutive natural numbers as [tex]\( x \)[/tex], [tex]\( x+1 \)[/tex], [tex]\( x+2 \)[/tex], and [tex]\( x+3 \)[/tex].
1. Write the equation for the sum of these numbers:
[tex]\[
x + (x + 1) + (x + 2) + (x + 3) = 98
\][/tex]
2. Combine like terms:
[tex]\[
x + x + 1 + x + 2 + x + 3 = 98
\][/tex]
3. Simplify the equation:
[tex]\[
4x + 6 = 98
\][/tex]
4. Isolate the variable [tex]\( x \)[/tex]:
- Subtract 6 from both sides of the equation:
[tex]\[
4x = 98 - 6
\][/tex]
- This simplifies to:
[tex]\[
4x = 92
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
- Divide both sides by 4:
[tex]\[
x = \frac{92}{4}
\][/tex]
6. Simplified result:
[tex]\[
x = 23
\][/tex]
7. Determine the four consecutive natural numbers:
- First number: [tex]\( x = 23 \)[/tex]
- Second number: [tex]\( x + 1 = 23 + 1 = 24 \)[/tex]
- Third number: [tex]\( x + 2 = 23 + 2 = 25 \)[/tex]
- Fourth number: [tex]\( x + 3 = 23 + 3 = 26 \)[/tex]
Therefore, the four consecutive natural numbers whose sum is 98 are:
[tex]\[
23, 24, 25, \text{and} 26
\][/tex]
