Peter and Catherine are selling cookies for a school fundraiser. They start selling on the same day. Peter starts with 300 cookies and sells them at an average of 15 boxes per day.

Question

The number of boxes of cookies, y, Catherine has left after x days is represented in the table shown.
x 0 1 2 3
y 300 250 200 150
Which statement is TRUE?

Peter's average rate of boxes of cookies sold per day is higher than Catherine's average rate
Catherine's average rate of boxes of cookies sold per day is higher than Peter's average rate
Catherine begins with more boxes of cookies than Peter
Peter begins with more boxes of cookies than Catherine

Answer 1

To determine the correct statement, we need to analyze the information provided for both Peter and Catherine regarding their cookies sold per day.

1. Peter's Sales:

   • Starts with: 300 cookies
   • Sells at an average rate of: 15 boxes per day

2. Catherine's Sales:

   • The table shows the number of boxes of cookies (y) she has left after x days:
     • Day 0: 300 cookies left
     • Day 1: 250 cookies left
     • Day 2: 200 cookies left
     • Day 3: 150 cookies left

   We can calculate Catherine's average rate of cookies sold per day:

   • From Day 0 to Day 1: 300 - 250 = 50 cookies sold in 1 day
   • From Day 1 to Day 2: 250 - 200 = 50 cookies sold in 1 day
   • From Day 2 to Day 3: 200 - 150 = 50 cookies sold in 1 day

   Thus, Catherine sells 50 boxes in total over 3 days, averaging about \( \frac{50 \text{ boxes}}{3 \text{ days}} \approx 16.67 \text{ boxes per day} \).

3. Comparison:

   • Peter's average rate: 15 boxes per day
   • Catherine's average rate: approximately 16.67 boxes per day

Now let's evaluate the statements:

• Statement 1: Peter's average rate of boxes of cookies sold per day is higher than Catherine's average rate. (FALSE)
• Statement 2: Catherine's average rate of boxes of cookies sold per day is higher than Peter's average rate. (TRUE)
• Statement 3: Catherine begins with more boxes of cookies than Peter. (FALSE)
• Statement 4: Peter begins with more boxes of cookies than Catherine. (FALSE)

The true statement is:

Catherine's average rate of boxes of cookies sold per day is higher than Peter's average rate.