Subjects algebra

Printer Rates

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We need to compare the printing rates of two printer models: a solid ink printer and a laser printer, to determine which prints faster and how many pages the faster printer can print in 2 minutes. 2. **Formula for rate:** Printing rate is pages per minute, calculated as $$\text{Rate} = \frac{\text{Pages}}{\text{Time (minutes)}}$$ 3. **Calculate the solid ink printer rate:** It prints 65 pages in 5 minutes. $$\text{Rate}_{solid} = \frac{65}{5} = 13 \text{ pages per minute}$$ 4. **Calculate the laser printer rate:** Use the data points from the table. - At 1.5 minutes, 21 pages: $$\frac{21}{1.5} = 14 \text{ pages per minute}$$ - At 3.5 minutes, 49 pages: $$\frac{49}{3.5} = 14 \text{ pages per minute}$$ - At 4.5 minutes, 63 pages: $$\frac{63}{4.5} = 14 \text{ pages per minute}$$ The laser printer consistently prints at 14 pages per minute. 5. **Compare rates:** - Solid ink printer: 13 pages per minute - Laser printer: 14 pages per minute The laser printer prints faster. 6. **Calculate pages printed by the laser printer in 2 minutes:** $$\text{Pages} = \text{Rate} \times \text{Time} = 14 \times 2 = 28$$ pages **Final answer:** The laser printer prints faster and can print 28 pages in 2 minutes.