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The sum of two numbers is

at least 5, and the sum of

the first number and 2 times

the second number is at

most 10. What are the

possible numbers?

1 Answer

0 votes

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.

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