Inequalities Graphs and Word Problems

Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

• 2x + 3y > 100

  x + y ≤ 40

• 100x + 2y > 3

  x + y ≤ 40

• 100x + 40y > 100

  3x + 2y ≤ 40

• 3x + 2y > 100

  x + y ≤ 40

Which of the following equations match the given graph?

• y ≥ 2/5x + 1

• y ≥ -2/5x + 1

• y≤  2/5x + 1

• y ≥ -2/5x - 1

This system has an infinite number of solutions, TRUE or FALSE?

• TRUE

• FALSE

Solve the system of inequalities by graphing.

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Mr. Shah is ordering chicken wings and fries for his son’s birthday party and has a budget of $81. An order of a bucket of chicken wings costs $13 and an order of basket of fries costs $7. Inequality: 13x+7y≤81 b) Graph in Desmos!! c) Choose all possible solutions below:

• 3 buckets of chicken wings & 2 baskets of fries

• 5 buckets of chicken wings &

  1 basket of fries

• 10 buckets of chicken wings &

  0 baskets of fries

• 0 buckets of chicken wings &

  10 baskets of fries

• 5 buckets of chicken wings &

  5 baskets of fries

Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which one of these is a valid solution?

• (3, 2)

• (1, 4)

• (2, 8)

• (5, 1)

Which point is not a solution?

• (1, 3)

• (-1, 2)

• (3, -2)

• (5, 0)

Which of the following equations match the given graph?

• y ≥ 2/5x + 1

• y ≥ -2/5x + 1

• y≤  2/5x + 1

• y ≥ -2/5x - 1

Select the correct graph for each inequality.

• A

• B

• C

• D

Is (0, 0) a solution to this inequality?

• Yes

• No