The problem you're working on involves Corey buying cookies and oranges, and it asks you to select the correct equation or tape diagram representing the situation.

Given Information:

• Corey spends a total of $28.11.
• He spends $6.75 on cookies.
• He buys 6 bags of oranges, with each bag costing the same amount (denoted by b).

To Model This Situation:

• The total amount Corey spends is the sum of what he pays for cookies and oranges.
• The total amount spent on oranges is the cost per bag (denoted as b) multiplied by the number of bags (6).

The equation can be written as: $28.11 = 6.75 + 6b$ This represents:

• $28.11 as the total Corey spends,
• $6.75 for the cookies,
• 6b as the total for 6 bags of oranges, where each bag costs b.

Option A:

$28.11 = 6 + 6.75b$ This equation seems incorrect because it mixes up the cost of cookies and oranges.

Option B:

A tape diagram shows 6b for the oranges and $6.75 for the cookies, adding up to $28.11. The tape diagram corresponds to the correct representation, matching the equation: $28.11 = 6.75 + 6b$

Option C:

This option simply shows the total amount of $28.11 without specifying how it is broken down, so it isn't very useful in representing the equation.

Conclusion:

The correct answer is B (the tape diagram), as it visually and mathematically represents the situation accurately.

Would you like further explanation or any details?

Here are 5 questions for practice:

1. How would the equation change if Corey bought 7 bags of oranges instead of 6?
2. If Corey spent $8 on cookies, how would that affect the equation?
3. What if each bag of oranges cost $2, how would you solve for b?
4. How does a tape diagram help in visualizing algebraic problems?
5. Could you write a similar word problem using a different item like apples?

Tip: Always start by identifying variables for unknowns and constants for known amounts when solving word problems!