Question 1191395
**(a) System of Inequalities**

Let 'b' represent the number of bananas and 'g' represent the number of granola bars.

* **Calorie Inequality:** Jocelyn needs at least 400 extra calories.
   90b + 150g ≥ 400

* **Budget Inequality:** Jocelyn has a budget of $15.
   0.35b + 2.50g ≤ 15

* **Non-Negative Inequalities:**  Jocelyn can't buy a negative number of bananas or granola bars.
   b ≥ 0
   g ≥ 0

Therefore, the system of inequalities is:  **90b + 150g ≥ 400, 0.35b + 2.50g ≤ 15, b ≥ 0, g ≥ 0**

**(b) Graphing the System**

I can't draw a graph here, but I'll describe how to graph it:

1. **Convert to Slope-Intercept Form (for easier graphing):**
   * Calorie Inequality: 150g ≥ -90b + 400  =>  g ≥ (-3/5)b + (8/3)
   * Budget Inequality: 2.50g ≤ -0.35b + 15  => g ≤ (-7/50)b + 6

2. **Plot the Lines:**
   * For g ≥ (-3/5)b + (8/3), plot the line g = (-3/5)b + (8/3).  Since it's "greater than or equal to," shade the area *above* this line.
   * For g ≤ (-7/50)b + 6, plot the line g = (-7/50)b + 6. Since it's "less than or equal to," shade the area *below* this line.
   * Also, remember b ≥ 0 and g ≥ 0, which means you're only considering the first quadrant (positive b and g values).

3. **Solution Region:** The solution region is where all the shaded areas overlap.  This represents the possible combinations of bananas and granola bars that meet Jocelyn's requirements.

**(c) 6 Bananas and 6 Granola Bars?**

* Calories: 90(6) + 150(6) = 540 + 900 = 1440 calories (meets the calorie need)
* Cost: 0.35(6) + 2.50(6) = 2.10 + 15 = $17.10 (exceeds the budget)

No, she could not buy 6 bananas and 6 granola bars because it exceeds her budget.

**(d) 3 Bananas and 3 Granola Bars?**

* Calories: 90(3) + 150(3) = 270 + 450 = 720 calories (meets the calorie need)
* Cost: 0.35(3) + 2.50(3) = 1.05 + 7.50 = $8.55 (within the budget)

Yes, she could buy 3 bananas and 3 granola bars.