Question

1. Maya is selling bracelets and necklaces she made to make money for summer vacation. The bracelets cost $4 and the necklaces cost $5. She needs to make at least $75. Maya only has 8 bracelets total to sell. Choose the system of linear inequalities below that represents the situation.

a. 4y+5x≥75
x≤8

b. 4y+5x≤75
y≥8

c. 4x+5y≤75x≥8

d. 4x+5y≥75
x≤8
2.
A gardener has 90 square feet to plant carrots and tomatoes for the farmers market. The gardener can only plant one carrot plant or one tomato plant per square foot and they want to determine how many of each crop to plant. The gardener can makes $2 profit for carrots and $1 profit for tomatoes, but it takes the gardener approximately 3 minutes to harvest a carrot plant and only 1 minute to harvest a tomato plant. Wanting to keep the produce as fresh as possible, she only gives herself at most 120 minutes before the farmers market to pick as many plants as she can. For this problem let's assume x = carrots and y = tomatoes.

What are all the constraints (inequalities) we need to consider in this problem?
a.
x ≥ 0
y ≥ 0
x + y ≥ 90
3x + y ≥ 120
b. x ≥ 0
y ≥ 0
x + y ≤ 90
3x + y ≤ 120
c.
x ≥ 0
y ≥ 0
2x + y ≤ 90
3x + y ≤ 120
d.
x ≥ 0
y ≤ 0
x + y ≤ 90
x + 3y ≤ 120

Answer 1

1. B

2.D

Explanation:

x = $80 profit made if sold all carrots.

y = $120 if all tomatoes are sold.