Question
Mr. Hon purchases a new car every 4 years. Ms. Jasper purchases a new car every 6 years. They both purchased new cars this year. When will they next both purchase new cars in the same year? A in 2 years B. in 8 years c. In 12 years D. Ln 24 years
Ask by Fernandez Rodriquez. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
They will both purchase new cars in the same year in 12 years.
Solution
To determine when Mr. Hon and Ms. Jasper will both purchase new cars in the same year again, we need to find the **Least Common Multiple (LCM)** of their purchase cycles.
- **Mr. Hon** purchases a new car every **4 years**.
- **Ms. Jasper** purchases a new car every **6 years**.
**Step 1: Prime Factorization**
- \(4 = 2^2\)
- \(6 = 2 \times 3\)
**Step 2: Calculate LCM**
To find the LCM, take the highest power of each prime number present in the factorizations:
- \(2^2 \times 3 = 12\)
Therefore, the LCM of 4 and 6 is **12**.
**Conclusion:**
Mr. Hon and Ms. Jasper will both purchase new cars in the same year **12 years** from now.
**Answer:**
C. In 12 years
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find out when Mr. Hon and Ms. Jasper next purchase a new car in the same year, we need to determine the least common multiple (LCM) of their purchase cycles: 4 years for Mr. Hon and 6 years for Ms. Jasper. The LCM of 4 and 6 is 12, meaning they will both buy new cars together again in 12 years. So the answer is C. In 12 years. To kick it up a notch, picture yourself in a future where both Mr. Hon and Ms. Jasper are driving their shiny new cars side by side in 12 years! It’s like a synchronized dance of auto purchases, where you can almost hear the engines revving in unison. How cool would that be? Mark your calendar!
