Malia has​ $500 to purchase water bottles and pairs of socks for a fundraiser for her​ school's cross-country team. She needs to buy a total of at least 200 items without buying too many of just one item. The graph shows the possible number of water bottles and pairs of socks that Malia should​ buy, and the system of inequalities.

Question

x plus y greater than or equals 200x+y≥200
2 x plus 3 y less than or equals 5002x+3y≤500
The given system of inequalities only makes sense in the first quadrant. What two inequalities could be added to the system to indicate​ this? Explain.
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x plus y greater than or equals 200x+y≥2002 x plus 3 y less than or equals 5002x+3y≤500


x y graph
Question content area bottom
Part 1
The inequalities that should be added are enter your response here. These inequalities indicate that all values of x must be
negative
and all values of y must be
positive.
​(Type inequalities. Use a comma to separate answers as​ needed.)

Answer 1

To ensure that Malia only purchases non-negative quantities of water bottles and pairs of socks (which are represented by the variables \( x \) and \( y \)), you need to add the following inequalities to the system:

1. \( x \geq 0 \) (This indicates that the number of water bottles must be non-negative.)
2. \( y \geq 0 \) (This indicates that the number of pairs of socks must be non-negative.)

So, the complete answer is:

The inequalities that should be added are \( x \geq 0, y \geq 0 \).

These inequalities indicate that all values of \( x \) must be non-negative and all values of \( y \) must be non-negative.