Answer :
To find the first number in the sequence of two consecutive numbers whose sum is 157, you can follow these steps:
1. Understand the problem: You have two consecutive numbers. If the first number is [tex]\( n \)[/tex], the next consecutive number would be [tex]\( n + 1 \)[/tex].
2. Set up the equation: According to the problem, these two numbers add up to 157. Therefore, the equation is:
[tex]\[
n + (n + 1) = 157
\][/tex]
3. Simplify the equation: Combine the terms with [tex]\( n \)[/tex].
[tex]\[
n + n + 1 = 157
\][/tex]
This simplifies to:
[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]
- Simplify the right side:
[tex]\[
2n = 156
\][/tex]
- Divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]
- Calculate the value:
[tex]\[
n = 78
\][/tex]
So, the first number is 78. Therefore, the correct answer is B. 78.
1. Understand the problem: You have two consecutive numbers. If the first number is [tex]\( n \)[/tex], the next consecutive number would be [tex]\( n + 1 \)[/tex].
2. Set up the equation: According to the problem, these two numbers add up to 157. Therefore, the equation is:
[tex]\[
n + (n + 1) = 157
\][/tex]
3. Simplify the equation: Combine the terms with [tex]\( n \)[/tex].
[tex]\[
n + n + 1 = 157
\][/tex]
This simplifies to:
[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]
- Simplify the right side:
[tex]\[
2n = 156
\][/tex]
- Divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]
- Calculate the value:
[tex]\[
n = 78
\][/tex]
So, the first number is 78. Therefore, the correct answer is B. 78.
