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Answer :
To find the first number, we need to understand the given situation: the sum of two consecutive numbers is 157. We are given the equation where [tex]\( n \)[/tex] is the first number:
[tex]\[ 2n + 1 = 157 \][/tex]
This equation represents the sum of the first number ([tex]\( n \)[/tex]) and the next consecutive number ([tex]\( n + 1 \)[/tex]), expressed as:
- First number: [tex]\( n \)[/tex]
- Second number: [tex]\( n + 1 \)[/tex]
So, their sum is:
[tex]\[ n + (n + 1) = 2n + 1 \][/tex]
Now, let's solve the equation [tex]\( 2n + 1 = 157 \)[/tex]:
1. Subtract 1 from both sides of the equation:
[tex]\[ 2n = 157 - 1 \][/tex]
[tex]\[ 2n = 156 \][/tex]
2. Divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{156}{2} \][/tex]
[tex]\[ n = 78 \][/tex]
Therefore, the first number is 78. The correct answer is:
B. 78
[tex]\[ 2n + 1 = 157 \][/tex]
This equation represents the sum of the first number ([tex]\( n \)[/tex]) and the next consecutive number ([tex]\( n + 1 \)[/tex]), expressed as:
- First number: [tex]\( n \)[/tex]
- Second number: [tex]\( n + 1 \)[/tex]
So, their sum is:
[tex]\[ n + (n + 1) = 2n + 1 \][/tex]
Now, let's solve the equation [tex]\( 2n + 1 = 157 \)[/tex]:
1. Subtract 1 from both sides of the equation:
[tex]\[ 2n = 157 - 1 \][/tex]
[tex]\[ 2n = 156 \][/tex]
2. Divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{156}{2} \][/tex]
[tex]\[ n = 78 \][/tex]
Therefore, the first number is 78. The correct answer is:
B. 78
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