Answer :
To solve the problem of finding the first number in two consecutive numbers that sum up to 157, we can use the given equation:
[tex]\[2n + 1 = 157\][/tex]
Here’s a step-by-step solution:
1. Understand the equation: The equation [tex]\(2n + 1 = 157\)[/tex] describes the sum of two consecutive numbers. The first number is [tex]\(n\)[/tex], and since the numbers are consecutive, the second number is [tex]\(n + 1\)[/tex]. Therefore, the equation becomes:
[tex]\[ n + (n + 1) = 157 \][/tex]
Simplifying this gives us the equivalent equation:
[tex]\[ 2n + 1 = 157 \][/tex]
2. Isolate the variable [tex]\(n\)[/tex]: We want to solve for [tex]\(n\)[/tex]. Begin by subtracting 1 from both sides to isolate the term with [tex]\(n\)[/tex]:
[tex]\[ 2n + 1 - 1 = 157 - 1 \][/tex]
[tex]\[ 2n = 156 \][/tex]
3. Solve for [tex]\(n\)[/tex]: Now, divide both sides by 2 to solve for [tex]\(n\)[/tex]:
[tex]\[ n = \frac{156}{2} \][/tex]
[tex]\[ n = 78 \][/tex]
Thus, the first number is [tex]\(78\)[/tex].
So the correct answer is:
B. 78
[tex]\[2n + 1 = 157\][/tex]
Here’s a step-by-step solution:
1. Understand the equation: The equation [tex]\(2n + 1 = 157\)[/tex] describes the sum of two consecutive numbers. The first number is [tex]\(n\)[/tex], and since the numbers are consecutive, the second number is [tex]\(n + 1\)[/tex]. Therefore, the equation becomes:
[tex]\[ n + (n + 1) = 157 \][/tex]
Simplifying this gives us the equivalent equation:
[tex]\[ 2n + 1 = 157 \][/tex]
2. Isolate the variable [tex]\(n\)[/tex]: We want to solve for [tex]\(n\)[/tex]. Begin by subtracting 1 from both sides to isolate the term with [tex]\(n\)[/tex]:
[tex]\[ 2n + 1 - 1 = 157 - 1 \][/tex]
[tex]\[ 2n = 156 \][/tex]
3. Solve for [tex]\(n\)[/tex]: Now, divide both sides by 2 to solve for [tex]\(n\)[/tex]:
[tex]\[ n = \frac{156}{2} \][/tex]
[tex]\[ n = 78 \][/tex]
Thus, the first number is [tex]\(78\)[/tex].
So the correct answer is:
B. 78
