To solve this problem, you need to set up two equations based on the information provided:

1. The total weight of oranges and grapefruits is 8 pounds. $x + y = 8$ Here, $x$ represents the number of pounds of grapefruit, and $y$ represents the number of pounds of oranges.

2. The total cost of the oranges and grapefruits is $10.35. The cost per pound for grapefruit is $1.20, and for oranges, it is $1.50. Therefore, the cost equation would be: $1.20x + 1.50y = 10.35$

So, the system of equations is:

x + y = 8 \\ 1.20x + 1.50y = 10.35 \end{cases}$$ Would you like help solving this system of equations or more details on how to approach it? ### Expanding on the problem, here are 5 related questions: 1. What is the value of $$x$$ (the pounds of grapefruit) and $$y$$ (the pounds of oranges)? 2. If the cost per pound of oranges increased to $1.75, how would that change the system of equations? 3. What would the system of equations be if the total weight was 10 pounds instead of 8? 4. How much would 5 pounds of each fruit cost at the given prices? 5. What if you had purchased 10.35 pounds of fruit but still paid $10.35? ### Tip: To solve systems of equations, substitution and elimination methods are two powerful techniques that can simplify complex problems like this one!