Printer A has a greater rate than Printer B. Both printers print at a constant rate.

Question

This table represents Printer A.

Time (min) 1 3 5 8
Number of pages printed 4.25 12.75 21.25 34
Which equation could represent Printer B?

Time in minutes is represented by x and number of pages printed is represented by y.

Select each correct answer.

Responses

y = 4.4x
y = 4.4 x

y = 4.2x
y = 4.2 x

y = 4.6x
y = 4.6 x

y = 4x

Answer 1

To determine the equation that represents Printer B, we first need to find the rate at which Printer A prints. We can calculate this by looking at the given data in the table.

First, let's find the average pages printed per minute for Printer A:

From the data in the table, we can calculate the rate using the total pages printed and the time at various points.

1. For 1 minute:

   • Pages printed: 4.25
   • Rate: \( \frac{4.25}{1} = 4.25 \) pages per minute

2. For 3 minutes:

   • Pages printed: 12.75
   • Rate: \( \frac{12.75}{3} = 4.25 \) pages per minute

3. For 5 minutes:

   • Pages printed: 21.25
   • Rate: \( \frac{21.25}{5} = 4.25 \) pages per minute

4. For 8 minutes:

   • Pages printed: 34
   • Rate: \( \frac{34}{8} = 4.25 \) pages per minute

The rate for Printer A is consistently 4.25 pages per minute.

Since Printer A has a greater rate than Printer B (which means Printer B must print at a rate that is less than 4.25 pages per minute), we need to look for the correct equations representing Printer B that are less than 4.25.

Let's evaluate the options you provided:

1. \( y = 4.4x \) – Rates: 4.4 pages/min (greater than 4.25, not valid).
2. \( y = 4.2x \) – Rate: 4.2 pages/min (valid).
3. \( y = 4.6x \) – Rate: 4.6 pages/min (greater than 4.25, not valid).
4. \( y = 4x \) – Rate: 4 pages/min (valid).

Thus, the equations that could represent Printer B, considering its rate must be less than 4.25, are:

• \( y = 4.2x \)
• \( y = 4x \)

So, the correct responses are:

• \( y = 4.2x \)
• \( y = 4x \)