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Answer :
Sure! Let's solve the problem step-by-step.
We are asked to find three consecutive integers whose sum is 489.
Step 1: Define the three consecutive integers.
Let the first integer be [tex]\( n \)[/tex].
Then the next two consecutive integers will be [tex]\( n+1 \)[/tex] and [tex]\( n+2 \)[/tex].
Step 2: Write the equation representing their sum.
The sum of these three integers is:
[tex]\[ n + (n + 1) + (n + 2) = 489 \][/tex]
Step 3: Simplify the equation.
Combine like terms:
[tex]\[ n + n + 1 + n + 2 = 489 \][/tex]
[tex]\[ 3n + 3 = 489 \][/tex]
Step 4: Solve the equation for [tex]\( n \)[/tex].
First, subtract 3 from both sides to isolate terms involving [tex]\( n \)[/tex]:
[tex]\[ 3n + 3 - 3 = 489 - 3 \][/tex]
[tex]\[ 3n = 486 \][/tex]
Next, divide both sides by 3:
[tex]\[ \frac{3n}{3} = \frac{486}{3} \][/tex]
[tex]\[ n = 162 \][/tex]
Step 5: Find the three consecutive integers.
Now that we have [tex]\( n = 162 \)[/tex],
- The first integer is [tex]\( 162 \)[/tex]
- The second integer is [tex]\( 162 + 1 = 163 \)[/tex]
- The third integer is [tex]\( 162 + 2 = 164 \)[/tex]
So, the three consecutive integers are 162, 163, and 164, which corresponds to the last option:
[tex]\[ 162, 163, 164 \][/tex]
Therefore, the three consecutive integers whose sum is 489 are [tex]\( \boxed{162, 163, 164} \)[/tex].
We are asked to find three consecutive integers whose sum is 489.
Step 1: Define the three consecutive integers.
Let the first integer be [tex]\( n \)[/tex].
Then the next two consecutive integers will be [tex]\( n+1 \)[/tex] and [tex]\( n+2 \)[/tex].
Step 2: Write the equation representing their sum.
The sum of these three integers is:
[tex]\[ n + (n + 1) + (n + 2) = 489 \][/tex]
Step 3: Simplify the equation.
Combine like terms:
[tex]\[ n + n + 1 + n + 2 = 489 \][/tex]
[tex]\[ 3n + 3 = 489 \][/tex]
Step 4: Solve the equation for [tex]\( n \)[/tex].
First, subtract 3 from both sides to isolate terms involving [tex]\( n \)[/tex]:
[tex]\[ 3n + 3 - 3 = 489 - 3 \][/tex]
[tex]\[ 3n = 486 \][/tex]
Next, divide both sides by 3:
[tex]\[ \frac{3n}{3} = \frac{486}{3} \][/tex]
[tex]\[ n = 162 \][/tex]
Step 5: Find the three consecutive integers.
Now that we have [tex]\( n = 162 \)[/tex],
- The first integer is [tex]\( 162 \)[/tex]
- The second integer is [tex]\( 162 + 1 = 163 \)[/tex]
- The third integer is [tex]\( 162 + 2 = 164 \)[/tex]
So, the three consecutive integers are 162, 163, and 164, which corresponds to the last option:
[tex]\[ 162, 163, 164 \][/tex]
Therefore, the three consecutive integers whose sum is 489 are [tex]\( \boxed{162, 163, 164} \)[/tex].
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