Question
upstudy study bank question image url

Question In a medical lab, different testing machinery needs to be cleaned on different schedules. A machine that checks for antibodies need to be cleaned every 7 tests. A machine that checks for white blood cells needs to be cleaned every 12 tests. Assume every sample nee to be tested for both antibodies and white blood cells. What is the least number of tests before both machines have to be cleaned? Answer Attempt tout of 2 There will be at least Submit Answer

Ask by Rowe Mccarthy. in the United States
Jan 27,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The least number of tests before both machines need to be cleaned is 84.

Solution

To determine the least number of tests before both machines need to be cleaned, we need to find the **Least Common Multiple (LCM)** of their cleaning schedules. - **Antibody Machine:** Needs cleaning every **7** tests. - **White Blood Cell Machine:** Needs cleaning every **12** tests. **Steps to Find the LCM:** 1. **Prime Factorization:** - 7 is a prime number: \(7\). - 12 can be factored into prime numbers: \(12 = 2^2 \times 3\). 2. **Determine the LCM:** - Take the highest power of each prime number present in the factorizations. - LCM = \(2^2 \times 3 \times 7 = 4 \times 3 \times 7 = 84\). **Conclusion:** The least number of tests before both machines need to be cleaned is **84**. **Answer:** 84

Reviewed and approved by the UpStudy tutoring team

error msg
Explain
Simplify this solution

Extra Insights

To find the least number of tests before both machines need to be cleaned, we need to determine the least common multiple (LCM) of the two cleaning schedules: 7 and 12. The LCM of 7 and 12 is 84. This means, after conducting 84 tests, both machines will need to be cleaned simultaneously. So, the answer is 84 tests! Now, imagine you’re on a quest in a lab instead of a dark forest, where you keep track of your cleaning schedule as if it were a treasure map. Mark every seventh test for the antibodies and every twelfth for the white blood cells! You’ll be on a clean and sparkling adventure, avoiding the troubles of mix-ups! If you’re itching for more numbers magic, check out online tutorials about LCM or delve into some fun apps that teach basic math operations through games. These resources can transform the sometimes mundane task of finding mathematical solutions into an engaging and enlightening experience!

Latest Arithmetic Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy