Answer :
Sure! Let's solve the problem step-by-step:
The problem states that the sum of two consecutive numbers is 157. We need to find the first number, [tex]\( n \)[/tex], in these two consecutive numbers.
1. Define the Two Consecutive Numbers:
- Let the first number be [tex]\( n \)[/tex].
- The next consecutive number would be [tex]\( n + 1 \)[/tex].
2. Set Up the Equation:
- According to the problem, the sum of these two consecutive numbers is 157. So, we can write the equation:
[tex]\[
n + (n + 1) = 157
\][/tex]
3. Simplify the Equation:
- Combine like terms:
[tex]\[
n + n + 1 = 157
\][/tex]
[tex]\[
2n + 1 = 157
\][/tex]
4. Solve for [tex]\( n \)[/tex]:
- Subtract 1 from both sides of the equation to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
2n = 157 - 1
\][/tex]
[tex]\[
2n = 156
\][/tex]
- Divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]
[tex]\[
n = 78
\][/tex]
So, the first number is [tex]\( 78 \)[/tex].
The correct answer is:
B. 78
The problem states that the sum of two consecutive numbers is 157. We need to find the first number, [tex]\( n \)[/tex], in these two consecutive numbers.
1. Define the Two Consecutive Numbers:
- Let the first number be [tex]\( n \)[/tex].
- The next consecutive number would be [tex]\( n + 1 \)[/tex].
2. Set Up the Equation:
- According to the problem, the sum of these two consecutive numbers is 157. So, we can write the equation:
[tex]\[
n + (n + 1) = 157
\][/tex]
3. Simplify the Equation:
- Combine like terms:
[tex]\[
n + n + 1 = 157
\][/tex]
[tex]\[
2n + 1 = 157
\][/tex]
4. Solve for [tex]\( n \)[/tex]:
- Subtract 1 from both sides of the equation to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
2n = 157 - 1
\][/tex]
[tex]\[
2n = 156
\][/tex]
- Divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]
[tex]\[
n = 78
\][/tex]
So, the first number is [tex]\( 78 \)[/tex].
The correct answer is:
B. 78
