Question

Let m, n, and p be integers such that mn=p, np=m, and MP=n. What is the sum of all the numbers in all of the possible ordered triples?

Answer 1

To find the sum of all the numbers in all of the possible ordered triples, solve the given equations and determine the values of n and p that satisfy the condition p^3 = n.

Step-by-step explanation:

In the given question, we are given three equations:

1. mn = p
2. np = m
3. mp = n

To find the sum of all the numbers in all of the possible ordered triples, we need to solve these equations.

From equation 1, we have:

m = p/n

Substituting this value of m in equation 2, we get:

np = p/n

np^2 = 1

p^3 = n

Similarly, substituting the value of p in equation 3:

(p/n)p = n

p^2 = n^2

So, the possible triples are (n, p, p^2) where p^3 = n.

The sum of all the numbers in all the possible ordered triples is the sum of all the values of n, p, and p^2 that satisfy the condition p^3 = n. Unfortunately, without additional information, we cannot determine the exact values of n and p that satisfy this condition.