Understanding Systems of Inequalities

The video tutorial covers two mathematical problems involving systems of inequalities. The first problem involves determining the maximum number of apples and bananas John can buy without exceeding a budget. The second problem involves calculating the dimensions of a rectangular fence Megan wants to build, ensuring the perimeter does not exceed a certain length while the area remains above a minimum threshold. The tutorial guides viewers through identifying variables, formulating inequalities, and eliminating incorrect answer choices to find the correct solutions.

What is the maximum number of fruits John can buy?

• 35

• 30

• 25

• 20

Which inequality represents the constraint on the number of fruits John can buy?

• a + b ≥ 30

• a + b > 30

• a + b ≤ 30

• a + b < 30

What is the cost of one apple in cents?

• 65

• 55

• 45

• 35

Which inequality represents the cost constraint for John's purchase?

• 0.45a + 0.65b < 16

• 0.45a + 0.65b ≤ 16

• 0.45a + 0.65b > 16

• 0.45a + 0.65b ≥ 16

What is the maximum perimeter Megan wants for her fence?

• 400 feet

• 550 feet

• 450 feet

• 500 feet

Which inequality represents the perimeter constraint for Megan's fence?

• 2l + 2w < 500

• 2l + 2w ≥ 500

• 2l + 2w > 500

• 2l + 2w ≤ 500

What is the minimum area Megan wants for her land?

• 12,000 sq ft

• 13,000 sq ft

• 14,000 sq ft

• 15,000 sq ft

Which inequality represents the area constraint for Megan's land?

• lw ≤ 14,000

• lw > 14,000

• lw ≥ 14,000

• lw < 14,000

If Megan divides the perimeter by 2, what is the new inequality?

• l + w < 250

• l + w ≥ 250

• l + w ≤ 250

• l + w > 250

Which answer choice is correct for Megan's problem based on the given constraints?

• C

• B

• A

• D