1. **State the problem:** We need to determine which machine produces juice boxes at a faster rate and then find how many juice boxes that faster machine produces in 30 minutes. 2. **Given data:** - Triton XZ produces 3,850 juice boxes in 14 minutes. - Rockner 2.0's production is shown by a line graph starting near (0,0) and reaching about 2,700 juice boxes at 10 minutes. 3. **Find the rate of production for each machine:** - Rate is calculated as $$\text{rate} = \frac{\text{juice boxes}}{\text{time in minutes}}$$ 4. **Calculate Triton XZ's rate:** $$\text{rate}_{\text{Triton}} = \frac{3850}{14} \approx 275 \text{ juice boxes per minute}$$ 5. **Calculate Rockner 2.0's rate from the graph:** - At 10 minutes, Rockner 2.0 produces about 2,700 juice boxes. $$\text{rate}_{\text{Rockner}} = \frac{2700}{10} = 270 \text{ juice boxes per minute}$$ 6. **Compare the rates:** - Triton XZ: 275 juice boxes/min - Rockner 2.0: 270 juice boxes/min Triton XZ produces juice boxes at a slightly faster rate. 7. **Calculate how many juice boxes Triton XZ produces in 30 minutes:** $$\text{juice boxes} = \text{rate} \times \text{time} = 275 \times 30 = 8250$$ **Final answer:** - Triton XZ produces juice boxes faster. - In 30 minutes, Triton XZ produces 8,250 juice boxes.