To solve the problem of finding two numbers given their sum and the difference between them, follow these detailed steps:
1. Let’s Define the Variables:
- Let [tex]\( x \)[/tex] be the smaller number.
- Since one number is 68 more than the other, the larger number will be [tex]\( x + 68 \)[/tex].
2. Set Up the Equation:
- According to the problem, the sum of the two numbers is 140.
- This can be written as:
[tex]\[
x + (x + 68) = 140
\][/tex]
3. Simplify the Equation:
- Combine like terms:
[tex]\[
2x + 68 = 140
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- First, isolate the term with [tex]\( x \)[/tex] by subtracting 68 from both sides of the equation:
[tex]\[
2x = 140 - 68
\][/tex]
- Simplify the right side:
[tex]\[
2x = 72
\][/tex]
- Now, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{72}{2} = 36
\][/tex]
5. Find the Larger Number:
- The larger number is 68 more than the smaller number.
- So, the larger number is:
[tex]\[
36 + 68 = 104
\][/tex]
Thus, the smaller number is 36 and the larger number is 104.
- The larger number is 104.
- The smaller number is 36.
