Question

Peter and Catherine are selling cookies for a school fundraiser. They start selling on the same day.

• Peters starts with 300 boxes of cookies and sells them at an average of 15 boxes per day.

• 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?
Responses

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

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

C Catherine begins with more boxes of cookies than Peter. Catherine begins with more boxes of cookies than Peter.

D Peter begins with more boxes of cookies than Catherine. Peter begins with more boxes of cookies than Catherine.

Answer 1

To determine which statement is true, let's analyze Peter's and Catherine's cookie sales:

1. **Peter's Cookie Sales:**
- Starts with 300 boxes.
- Sells 15 boxes per day.

To find out how many boxes Peter has left after a certain number of days (x), we can use the formula:
\[
\text{Boxes left} = 300 - 15x
\]

2. **Catherine's Cookie Sales:**
- The data provided in the table is as follows:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & 300 \\
1 & 250 \\
2 & 200 \\
3 & 150 \\
\hline
\end{array}
\]

From the table, we see:
- At day 0, Catherine has 300 boxes.
- At day 1, Catherine has 250 boxes (sold 50 boxes).
- At day 2, Catherine has 200 boxes (sold another 50 boxes).
- At day 3, Catherine has 150 boxes (sold another 50 boxes).

From this data, we can see that Catherine sells 50 boxes per day.

3. **Now we can compare:**
- **Peter's rate:** 15 boxes/day
- **Catherine's rate:** 50 boxes/day

Based on this information, we can evaluate the responses:

A: **Peter’s average rate of boxes of cookies sold per day is higher than Catherine’s average rate.**
**(False; Peter's rate is 15 boxes/day, while Catherine's is 50 boxes/day.)**

B: **Catherine’s average rate of boxes of cookies sold per day is higher than Peter’s average rate.**
**(True; Catherine sells 50 boxes/day while Peter sells 15 boxes/day.)**

C: **Catherine begins with more boxes of cookies than Peter.**
**(False; both started with 300 boxes.)**

D: **Peter begins with more boxes of cookies than Catherine.**
**(False; both started with 300 boxes.)**

The true statement is **B: Catherine’s average rate of boxes of cookies sold per day is higher than Peter’s average rate.**