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Answer :
To find the first number of two consecutive numbers whose sum is 157, let's break down the problem step by step.
1. Understand Consecutive Numbers:
- Two consecutive numbers can be represented as [tex]\( n \)[/tex] and [tex]\( n+1 \)[/tex]. For example, if the first number is 5, the next consecutive number is 6.
2. Set Up the Equation:
- According to the problem, the sum of these two numbers is 157.
- So, we write the equation for their sum: [tex]\( n + (n + 1) = 157 \)[/tex].
3. Simplify the Equation:
- Combine like terms: [tex]\( n + n + 1 = 2n + 1 \)[/tex].
- So, the equation becomes: [tex]\( 2n + 1 = 157 \)[/tex].
4. Solve for [tex]\( n \)[/tex]:
- To find [tex]\( n \)[/tex], start by subtracting 1 from both sides of the equation: [tex]\( 2n + 1 - 1 = 157 - 1 \)[/tex].
- This simplifies to: [tex]\( 2n = 156 \)[/tex].
- Divide both sides by 2 to solve for [tex]\( n \)[/tex]: [tex]\( n = 156 \div 2 \)[/tex].
- Hence, [tex]\( n = 78 \)[/tex].
5. Conclusion:
- The first number, [tex]\( n \)[/tex], is 78.
So, the correct answer is B. 78.
1. Understand Consecutive Numbers:
- Two consecutive numbers can be represented as [tex]\( n \)[/tex] and [tex]\( n+1 \)[/tex]. For example, if the first number is 5, the next consecutive number is 6.
2. Set Up the Equation:
- According to the problem, the sum of these two numbers is 157.
- So, we write the equation for their sum: [tex]\( n + (n + 1) = 157 \)[/tex].
3. Simplify the Equation:
- Combine like terms: [tex]\( n + n + 1 = 2n + 1 \)[/tex].
- So, the equation becomes: [tex]\( 2n + 1 = 157 \)[/tex].
4. Solve for [tex]\( n \)[/tex]:
- To find [tex]\( n \)[/tex], start by subtracting 1 from both sides of the equation: [tex]\( 2n + 1 - 1 = 157 - 1 \)[/tex].
- This simplifies to: [tex]\( 2n = 156 \)[/tex].
- Divide both sides by 2 to solve for [tex]\( n \)[/tex]: [tex]\( n = 156 \div 2 \)[/tex].
- Hence, [tex]\( n = 78 \)[/tex].
5. Conclusion:
- The first number, [tex]\( n \)[/tex], is 78.
So, the correct answer is B. 78.
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