Answer:
Let's call the two numbers x and y. Then, we can set up the following system of inequalities based on the given information:
x + y ≥ 5 (the sum of the two numbers is at least 5)
x + 2y ≤ 10 (the sum of the first number and 2 times the second number is at most 10)
To solve for the possible values of x and y, we can use algebra.
First, we can rearrange the second inequality to solve for x:
x ≤ 10 - 2y
Then, we can substitute this expression for x into the first inequality:
10 - 2y + y ≥ 5
Simplifying, we get:
y ≤ 5
Substituting this inequality back into the first inequality, we can solve for x:
x ≥ 5 - y
Combining these two expressions for x and y, we get:
5 - y ≤ x ≤ 10 - 2y
Therefore, the possible values for x and y that satisfy the given conditions are all pairs of numbers where x is between 5 - y and 10 - 2y, and y is less than or equal to 5.