To determine which statement is true, let's analyze Peter's and Catherine's cookie sales:
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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: \[ \text{Boxes left} = 300 - 15x \]
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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.
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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.
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