Answer :
To find three consecutive odd integers whose sum is 147, we need to choose the correct equation. Let's break down the options:
1. Option 1: [tex]\(n + n + n = 147\)[/tex]
- This equation assumes all three numbers are the same, which doesn't represent consecutive odd integers.
2. Option 2: [tex]\(n + (n + 1) + (n + 2) = 147\)[/tex]
- This equation represents three consecutive integers, not necessarily odd integers. Consecutive integers are just one unit apart, while consecutive odd integers are two units apart.
3. Option 3: [tex]\(n + (n + 1) + (n + 3) = 147\)[/tex]
- This equation also doesn't work for odd integers. It skips around but does not consistently add up to odd numbers.
4. Option 4: [tex]\(n + (n + 2) + (n + 4) = 147\)[/tex]
- This equation correctly represents three consecutive odd integers. Starting with [tex]\(n\)[/tex] (an odd integer), the next odd integers would be [tex]\(n + 2\)[/tex] and [tex]\(n + 4\)[/tex].
Therefore, the correct equation to find three consecutive odd integers whose sum is 147 is Option 4: [tex]\(n + (n + 2) + (n + 4) = 147\)[/tex].
1. Option 1: [tex]\(n + n + n = 147\)[/tex]
- This equation assumes all three numbers are the same, which doesn't represent consecutive odd integers.
2. Option 2: [tex]\(n + (n + 1) + (n + 2) = 147\)[/tex]
- This equation represents three consecutive integers, not necessarily odd integers. Consecutive integers are just one unit apart, while consecutive odd integers are two units apart.
3. Option 3: [tex]\(n + (n + 1) + (n + 3) = 147\)[/tex]
- This equation also doesn't work for odd integers. It skips around but does not consistently add up to odd numbers.
4. Option 4: [tex]\(n + (n + 2) + (n + 4) = 147\)[/tex]
- This equation correctly represents three consecutive odd integers. Starting with [tex]\(n\)[/tex] (an odd integer), the next odd integers would be [tex]\(n + 2\)[/tex] and [tex]\(n + 4\)[/tex].
Therefore, the correct equation to find three consecutive odd integers whose sum is 147 is Option 4: [tex]\(n + (n + 2) + (n + 4) = 147\)[/tex].
