The given graph and equation are based on the equation $7.5x + 10y = 400$, where $x$ represents the number of Italian submarine sandwiches, and $y$ represents the number of ham submarine sandwiches a student needs to sell to pay for their school trip. The task involves interpreting the graph to see which statements are true.

Breakdown of the Equation:

1. $7.5x + 10y = 400$: This represents the cost for selling x Italian sandwiches (at $7.50 each) and y ham sandwiches (at $10 each). The goal is to earn $400 to afford the trip.

Understanding the Graph:

• The points plotted, like (0,40), (16,28), (24,22), and so on, represent various combinations of x (Italian sandwiches) and y (ham sandwiches) that satisfy the equation.
• The graph shows the line of solutions where combinations of x and y make the total revenue equal to $400.

Analysis of the Options:

1. Option A:

   • If the student sells 20 Italian sandwiches and 20 ham sandwiches, plug these values into the equation: $7.5(20) + 10(20) = 150 + 200 = 350$ They would not reach $400, so this statement is false.

2. Option B:

   • Selling 55 Italian sandwiches: $7.5(55) = 412.5$ This exceeds $400, so the student would indeed have enough. True.

3. Option C:

   • If 30 Italian sandwiches are sold, how many ham sandwiches are needed? $7.5(30) + 10y = 400 \implies 225 + 10y = 400 \implies 10y = 175 \implies y = 17.5$ So, more than 15 ham sandwiches are needed. True.

4. Option D:

   • The cost per Italian sandwich is $7.50, not $10. False.

5. Option E:

   • This statement is just a description of the line, which represents combinations of x and y that yield $400. True.

Conclusion:

• True Statements: B, C, E.

Would you like further details or clarifications on any part? Here are 5 related questions:

1. What is the slope of the line representing this equation?
2. How many sandwiches of one type would need to be sold if no sandwiches of the other type are sold?
3. Can this scenario be modeled with a system of inequalities if the student must exceed $400?
4. How can you calculate the intercepts of this equation?
5. What would happen if the prices of sandwiches increased by $2 each?

Tip: Always check if values from a word problem satisfy the given equation to verify answers.