Writing Systems of Inequalities - SAT Math Part 23

TL;DR

Learn how to create a system of inequalities to represent John's fruit purchase and Megan's fence building situations.

Transcript

81. john wants to buy atmos 30 fruits consistent of apples and bananas he does not want to spend any more than 16 dollars if an apple costs 45 cents and a banana costs 65 cents which of the following system of inequalities represents john's situation would you say it's a b c or d how can we find out what should we do to get the answer well let's be... Read More

Key Insights

• 🛟 System of inequalities can be used to represent real-life situations involving constraints and conditions.
• 😑 Variables are used to represent quantities in the situations, allowing for mathematical expressions and inequalities.
• 🍌 In John's fruit purchasing situation, the total number of fruits and their cost are considered.
• 🖐️ In Megan's fence building situation, both the perimeter and the area of the land play a role.

Questions & Answers

Q: What do the variables "a" and "b" represent in John's fruit purchasing situation?

In John's situation, "a" represents the number of apples he wants to buy, while "b" represents the number of bananas he wants to buy.

Q: How do we represent John's condition of not buying more than 30 fruits in terms of inequalities?

We can express John's condition as "a + b ≤ 30," meaning that the total number of apples and bananas combined cannot exceed 30.

Q: What is the second inequality that represents John's condition of not spending more than $16?

The second inequality can be written as "0.45a + 0.65b ≤ 16," representing the cost of all the apples (0.45 cents each) plus the cost of all the bananas (0.65 cents each) not exceeding $16.

Q: Which answer choice represents the correct system of inequalities for John's situation?

Answer choice A is correct, as it matches both inequalities: "a + b ≤ 30" and "0.45a + 0.65b ≤ 16."

Q: What are the variables "l" and "w" used for in Megan's fence building situation?

In Megan's situation, "l" represents the length of the rectangular fence, and "w" represents the width of the fence.

Q: How is the perimeter of a rectangle calculated?

The perimeter of a rectangle is calculated by adding twice the length to twice the width, which gives the equation "2l + 2w."

Q: What is Megan's condition for the perimeter of the fence?

Megan's condition is that the perimeter of the fence should be less than or equal to 500 feet, expressed as "2l + 2w ≤ 500."

Q: What is the inequality representing Megan's condition for the area of the land enclosed by the fence?

The inequality representing Megan's condition for the area is "lw > 14,000," indicating that the product of the length and width must be greater than 14,000 square feet.

Summary & Key Takeaways

• John wants to buy a maximum of 30 fruits (apples and bananas combined), with the cost of each apple being 45 cents and each banana being 65 cents.

• The cost of all the apples plus the cost of all the bananas should not exceed $16.

• Megan wants to build a rectangular fence with a perimeter not exceeding 500 feet, while also ensuring that the area of the land enclosed by the fence is greater than 14,000 square feet.