Pregunta
The three numbers of the combination for a lock are consecutive integers, and their sum is 99. Find the combination. smallest value largest value SUBMIT ANSWER
Ask by Schneider Deleon. in the United States
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The smallest number is 32 and the largest number is 34.
Solución
Let's denote the three consecutive integers as \( x \), \( x+1 \), and \( x+2 \).
1. **Set up the equation for their sum:**
\[
x + (x + 1) + (x + 2) = 99
\]
2. **Combine like terms:**
\[
3x + 3 = 99
\]
3. **Subtract 3 from both sides:**
\[
3x = 96
\]
4. **Divide by 3:**
\[
x = 32
\]
Now we can find the three consecutive integers:
- The smallest integer is \( x = 32 \).
- The next integer is \( x + 1 = 33 \).
- The largest integer is \( x + 2 = 34 \).
Thus, the combination for the lock is:
- Smallest value: \( 32 \)
- Largest value: \( 34 \)
Final answer:
- Smallest value: 32
- Largest value: 34
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Extra Insights
To find the three consecutive integers whose sum is 99, you can set them as x, x+1, and x+2. Their sum would be: x + (x + 1) + (x + 2) = 99. This simplifies to 3x + 3 = 99, and then to 3x = 96, giving you x = 32. Thus, the three consecutive integers are 32, 33, and 34. The smallest value is 32. The largest value is 34. Happy locking!

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