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Answer :
To find the first number in the pair of consecutive numbers that sum to 157, we can follow these steps:
1. Let's denote the first number as [tex]\( n \)[/tex]. The next consecutive number would be [tex]\( n+1 \)[/tex].
2. According to the problem, the sum of these two consecutive numbers is 157. We can write this as an equation:
[tex]\[
n + (n + 1) = 157
\][/tex]
3. Simplify the equation:
[tex]\[
n + n + 1 = 157
\][/tex]
[tex]\[
2n + 1 = 157
\][/tex]
4. To solve for [tex]\( n \)[/tex], start by isolating [tex]\( 2n \)[/tex]. Subtract 1 from both sides of the equation:
[tex]\[
2n + 1 - 1 = 157 - 1
\][/tex]
[tex]\[
2n = 156
\][/tex]
5. Next, 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 78.
Therefore, the correct answer is:
[tex]\[
\boxed{78}
\][/tex]
1. Let's denote the first number as [tex]\( n \)[/tex]. The next consecutive number would be [tex]\( n+1 \)[/tex].
2. According to the problem, the sum of these two consecutive numbers is 157. We can write this as an equation:
[tex]\[
n + (n + 1) = 157
\][/tex]
3. Simplify the equation:
[tex]\[
n + n + 1 = 157
\][/tex]
[tex]\[
2n + 1 = 157
\][/tex]
4. To solve for [tex]\( n \)[/tex], start by isolating [tex]\( 2n \)[/tex]. Subtract 1 from both sides of the equation:
[tex]\[
2n + 1 - 1 = 157 - 1
\][/tex]
[tex]\[
2n = 156
\][/tex]
5. Next, 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 78.
Therefore, the correct answer is:
[tex]\[
\boxed{78}
\][/tex]
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