A package of 8 pens costs $1.09. Milo’s work to find the unit price of the pack is shown below.

Question

StartFraction 8 pens Over 1 dollar and 9 cents EndFraction = StartFraction question mark Over 1 dollar EndFraction. Question mark = StartFraction 8 Over 1 dollar and 9 cents EndFraction. Question mark = 7 dollars and 34 cents.

Where did Milo make his first error?
He assumed the pens are equally priced.
He wrote the unit rate incorrectly.
He made a place value error when dividing.
He multiplied instead of dividing.

Answer 1

Milo's first error was: He wrote the unit rate incorrectly.

To find the unit price of one pen, you need to divide the total cost by the number of pens. Therefore, the unit price calculation should be as follows:

1. The cost of the pack is $1.09.
2. There are 8 pens in the pack.

The correct calculation for the unit price of one pen is:

\[ \text{Unit Price} = \frac{1.09 \text{ dollars}}{8 \text{ pens}} = 0.13625 \text{ dollars/pen} \approx 0.14 \text{ dollars/pen} \]

Milo's equation implies that he used incorrect reasoning or arithmetic to derive the unit rate, specifically in interpreting or calculating the result as $7.34, which doesn't align with the calculations for unit price. Thus, he wrote the unit rate incorrectly.