High School

We appreciate your visit to For questions 23 28 use the following scenario Both Charlotte and Trey trade baseball cards The table below shows Charlotte s cards each week for. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

For questions 23-28, use the following scenario:

Both Charlotte and Trey trade baseball cards. The table below shows Charlotte's cards each week for a month. Trey started with a bunch of cards. After 2 weeks, Trey had a total of 250 cards, and after 4 weeks, Trey had a total of 370 cards.

**Charlotte's Cards by Week**

[tex]
\[
\begin{tabular}{|c|c|}
\hline
\text{Week} & \text{Total Baseball Cards} \\
\hline
1 & 470 \\
\hline
2 & 440 \\
\hline
3 & 410 \\
\hline
4 & 380 \\
\hline
\end{tabular}
\]
[/tex]

23. How many cards did Charlotte start out with at the beginning of the month?

24. How many cards is Trey getting per week?

25. What is the difference in the initial value of Charlotte's and Trey's cards?

26. What is the slope of the equation that would model Charlotte's change in cards per week?

27. How many combined cards would Charlotte and Trey have together in week 3?

28. If Charlotte and Trey kept trading at a constant rate, after 6 total weeks, how many more cards would Trey have than Charlotte?

Answer :

Let's solve each question step-by-step:

23. How many cards did Charlotte start out with at the beginning of the month?

Charlotte started with 470 cards at the beginning of the month, as shown in the table for week 1.

24. How many cards is Trey getting per week?

Trey's card count increased from 250 cards in week 2 to 370 cards in week 4. This means he gained 370 - 250 = 120 cards over these 2 weeks. Therefore, Trey is getting 120 cards / 2 weeks = 60 cards per week.

25. What is the difference in the initial value of Charlotte and Trey?

To find Trey’s initial card count, we can work back from week 2. Since Trey acquires 60 cards per week, the estimated number of cards at the start (week 1) would have been 250 - 60 = 190 cards. The difference between Charlotte's starting count and Trey's starting count is 470 - 190 = 280 cards.

26. What is the slope of the equation that would model Charlotte's change in cards per week?

Charlotte's card count decreased from 470 cards in week 1 to 380 cards in week 4. Over these 3 weeks, she lost 470 - 380 = 90 cards. The rate of change, or slope, is therefore 90 cards / 3 weeks = 30 cards per week. Since Charlotte is losing cards, the slope is negative: -30 cards per week.

27. How many combined cards would Charlotte and Trey have together in week 3?

In week 3, Charlotte has 410 cards. Meanwhile, Trey, starting with 250 cards in week 2, gains 60 cards by week 3, giving him a total of 250 + 60 = 310 cards. Combined, Charlotte and Trey have 410 + 310 = 720 cards in week 3.

28. If Charlotte and Trey kept trading at a constant rate, after 6 total weeks how many more cards would Trey have than Charlotte?

After 6 weeks, Charlotte would continue losing 30 cards per week from her starting count of 470, resulting in 470 - (30 x 5) = 320 cards. Trey, starting with an estimated initial count of 190 cards and gaining 60 cards per week, would have 190 + (60 x 6) = 550 cards after 6 weeks. The difference in the number of cards Trey has compared to Charlotte is 550 - 320 = 230 more cards.

I hope this breakdown helps you understand the solution! Let me know if you have any questions.

Thanks for taking the time to read For questions 23 28 use the following scenario Both Charlotte and Trey trade baseball cards The table below shows Charlotte s cards each week for. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada