Question

Sabina is baking cookies for a bake sale, but she wants to keep some for her friends to eat. Let x
represent the number of cookies to be sold at the bake sale and let y represent the number of
cookies to be shared with friends. Sabina wants to sell at least ten mmore than twice as many cookies
as she shares with friends. Sabina plans to make at most 120 cookies and wants to share between
10 and 20 of them with friends.
Write the system of inequalities that represents these constraints.

Answer 1

The inequalities represent the amount of cookies that can be expected to

be sold or shared with friends.

The system of inequalities that represent the given constraints are;

• x + y ≤ 120

• x ≥ 10 + 2·y

• 10 ≤ y ≤ 20

Reasons:

The number of cookies to be sold at the bake sale = x

Number of cookies to be shared with friends = y

The number of cookies Sabina wants to sell ≥ 10 + 2·y

The number of cookies Sabina wants to make = At most 120 cookies

Number of cookies she wants to share with friends = Between 10 and 20

Required:

To write the system of inequalities that represent the given constraints

Solution:

The system of inequalities are;

The number of cookies she makes = x + y ≤ 120

Number of cookies for sale, x ≥ 10 + 2·y

Number of cookies to be shared with friends is 10 ≤ y ≤ 20

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