carter reicieved his locker combo from his teacher. he noticed that each of th three intergers is prime, the sum of the three inteegers is 50, and three are in decreasing order. what is the valu eof the the last integer of carters locker combo

Let's solve this step by step.

Carter's locker combination consists of three integers that:
1. Are prime numbers.
2. Sum to 50.
3. Are arranged in decreasing order.

### Step 1: Identify prime numbers less than 50
Prime numbers less than 50 are:
\[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 \]

### Step 2: Find a combination of three primes whose sum is 50
We need to find three prime numbers from the list such that their sum is 50, and they are in decreasing order.

Let's start by trying different combinations:
- The largest prime number less than 50 is 47. If we take 47, the remaining two numbers must sum to \( 50 - 47 = 3 \), but no two primes sum to 3, so 47 is not part of the combination.
- Next, try 43. If we take 43, the remaining two numbers must sum to \( 50 - 43 = 7 \). The prime numbers that sum to 7 are \( 5 + 2 \).

So, the combination is \( 43, 5, 2 \), which are in decreasing order.

### Step 3: Verify the sum
\[
43 + 5 + 2 = 50
\]
The sum is correct.

### Conclusion:
The last integer in Carter's locker combination is **2**.

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Would you like more details on this solution or have any questions?

Here are five related questions to expand your understanding:
1. What are the properties of prime numbers?
2. How can you verify if a number is prime?
3. What other sets of prime numbers can sum to a different total?
4. Can you create a similar problem with a sum of 60 using primes?
5. How would the solution change if one number in the combination had to be even?

**Tip:** Prime numbers are only divisible by 1 and themselves, which makes them fundamental in number theory and cryptography!

Carter received his locker combo from his teacher. He noticed that each of the three integers is prime, the sum of the three integers is 50, and they are in decreasing order. What is the value of the last integer of Carter's locker combo?

Learn how to solve the prime number locker combination problem, where the sum of three prime numbers equals 50. This detailed explanation covers number theory, prime numbers, and their properties, making it ideal for students in Grades 6-8.

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