Let's analyze the given problem:

Mike has $40 to spend on oranges and grapes. The cost of each orange is $1.20, and the cost of each pound of grapes is $2.50. We are asked to create a linear equation that represents this situation, where:

• $o$ represents the number of oranges,
• $g$ represents the number of pounds of grapes,
• The total amount Mike spends on both oranges and grapes cannot exceed $40.

Now, the cost of oranges is $1.20o$ and the cost of grapes is $2.50g$. The total cost for oranges and grapes together is the sum of these two quantities, which must equal $40:

$1.20o + 2.50g = 40$

Thus, the correct equation is the fourth option: $40 = 1.20o + 2.50g$

Would you like more details, or do you have any further questions?

Here are some related questions to expand your understanding:

1. What is the slope of the linear equation representing Mike’s situation?
2. How would the equation change if Mike had $50 instead of $40?
3. If Mike buys 10 oranges, how many pounds of grapes can he buy with the remaining money?
4. What kind of graph would represent the relationship between the number of oranges and grapes Mike can buy?
5. How would the equation change if the cost of grapes were reduced to $2.00 per pound?

Tip: When solving problems involving costs and total amounts, setting up a proper equation with defined variables is key to finding a solution.