Randy wants to collect 515 baseballs cards. Each week Randy buys 15 baseball cards. a. Create a table to represent this situation where t is the amount of time in weeks and c is the number of cards that Randy still wants to buy. b. Write an equation to model the data in the table. c. Graph the equation. d. After how many weeks will Randy meet his goal?
so, did you build a table? see any patterns there?
a. To create a table representing this situation, we can start with the initial number of cards Randy wants to collect and then subtract 15 cards each week until reaching 0, which represents Randy meeting his goal. Here is the table:
| t | c |
|-----|-----|
| 0 | 515 |
| 1 | 500 |
| 2 | 485 |
| 3 | 470 |
| 4 | 455 |
| 5 | 440 |
| ... | ... |
| n | 0 |
In this table, t is the amount of time in weeks, and c represents the number of cards Randy still wants to buy.
b. To write an equation to model the data in the table, we can observe that the number of cards Randy still wants to buy decreases by 15 each week. Thus, we can use the equation:
c = 515 - 15t
In this equation, t represents the number of weeks elapsed, and c represents the number of cards Randy still wants to buy.
c. To graph the equation, we can plot the values from the table on a coordinate plane, where the x-axis represents the number of weeks (t), and the y-axis represents the number of cards Randy still wants to buy (c).
d. To find out after how many weeks Randy will meet his goal, we need to find the value of t when c becomes 0 in the equation. Substituting c = 0 into the equation, we have:
0 = 515 - 15t
Solving for t, we get:
15t = 515
t = 34.33 (approx)
Therefore, after approximately 34.33 weeks, Randy will meet his goal of collecting 515 baseball cards.