Inequalities and Application Problems

This video tutorial covers solving two application problems using inequalities in one variable. The first example involves determining the maximum number of credit hours a student can take for under $1,000, given a tuition cost of $76 per credit hour. The second example involves calculating the number of computers a business owner must sell to make a profit, considering fixed and variable costs. Both problems are solved step-by-step, emphasizing the importance of whole numbers in the solutions.

What is the main focus of this lesson?

• Solving equations with two variables

• Learning about quadratic equations

• Solving application problems using inequalities in one variable

• Understanding fractions and decimals

If the tuition cost is $76 per credit hour, what inequality represents the maximum number of credit hours a student can take for under $1,000?

• C/76 > 1000

• C/76 < 1000

• 76C < 1000

• 76C > 1000

After solving the inequality for the first example, what is the maximum whole number of credit hours a student can take?

• 14

• 13

• 15

• 12

Why must the number of credit hours be a whole number in the first example?

• Because the inequality only works with whole numbers

• Because students can only take full credit hours

• Because the tuition cost is a whole number

• Because fractions are not allowed in inequalities

What are the fixed operating costs for Sean's computer business per week?

• $600

• $2,700

• $3,000

• $1,500

What is the cost to produce each computer in Sean's business?

• $1,500

• $2,700

• $600

• $900

What is the selling price of each computer in Sean's business?

• $900

• $1,500

• $2,700

• $600

What inequality represents the condition for Sean to make a profit?

• 1500C > 2700 + 600C

• 1500C <= 2700 + 600C

• 1500C < 2700 + 600C

• 1500C = 2700 + 600C

How many computers must Sean sell to ensure a profit?

• 3

• 2

• 4

• 5

Why must the number of computers sold be a whole number in the second example?

• Because the fixed costs are whole numbers

• Because computers can only be sold in whole units

• Because the profit margin is a whole number

• Because the inequality only works with whole numbers