Let's analyze and solve the given problems step-by-step.

Problem 9:

Question: The total weight of a full container is 23.7 tons, while the container weighs 2.25 tons when it is empty. If each barrel weighs 0.11 tons, how many barrels does the container hold?

Choices:

• $2.25e + 0.11 = 23.7$
• $0.11b + 2.25 = 23.7$
• Let $e$ represent the number of empty barrels.
• Let $b$ represent the number of barrels.

Solution: The total weight of the container is made up of the empty container weight and the weight of the barrels inside. Let $b$ represent the number of barrels. Then:

$0.11b + 2.25 = 23.7$

So, the correct variable equation and representation are:

• $0.11b + 2.25 = 23.7$
• Let $b$ represent the number of barrels.

Problem 10:

Question: Teri earned $18.25 an hour at the semiconductor plant. The payroll deductions reduced her paycheck by $182.50. If her first weekly paycheck was at least $547.50 after the deductions, how many hours did she work that week?

Choices:

• $\frac{182.50}{h} \leq 547.50$
• Let $h$ represent the number of hours she worked that week.
• $18.25h - 182.50 \geq 547.50$
• $18.25h + 182.50 \geq 547.50$

Solution: To find the inequality representing the number of hours Teri worked, let's set up the equation for her total earnings before deductions. Let $h$ be the number of hours worked.

The total earnings before deductions are $18.25h$. After deducting $182.50, the paycheck needs to be at least $547.50. This can be represented by the inequality:

$18.25h - 182.50 \geq 547.50$

So, the correct inequality and variable representation are:

• $18.25h - 182.50 \geq 547.50$
• Let $h$ represent the number of hours she worked that week.

Summary:

For problem 9:

• Correct equation: $0.11b + 2.25 = 23.7$
• Correct variable: Let $b$ represent the number of barrels.

For problem 10:

• Correct inequality: $18.25h - 182.50 \geq 547.50$
• Correct variable: Let $h$ represent the number of hours she worked that week.

Would you like more details or have any questions?

Additional Practice Problems:

1. If each barrel weighs 0.2 tons instead of 0.11 tons, how many barrels would the container hold given the same conditions in problem 9?
2. What would be Teri's paycheck if she worked 35 hours, given the same conditions in problem 10?
3. How much more does Teri need to earn per hour to achieve a paycheck of $600 after the same deductions if she worked 40 hours?
4. If the weight of each barrel was reduced to 0.08 tons, how many barrels can the container hold under the same conditions in problem 9?
5. Suppose Teri worked 30 hours. What should be her hourly wage to achieve a paycheck of at least $500 after deductions?

Tip:

When solving equations or inequalities involving real-life scenarios, clearly define your variables and ensure your units are consistent throughout the problem.