Question

Felicia has 29 buttons in her collection.She will connect 12 new buttons every year.Felicia collects buttons for k years.For what values of k will Felicia have at least 120 buttons?

Answer 1

For Felicia to have at least 120 buttons, k will have to be greater than or equal to 8.

Here's how to find that.

I found it's easiest to create an X,Y table (or K,L table as shown in the image below). The X (K) value starts at 0 (the start of collection) and continues to go up by by 1 to account for every year she collects buttons, while the Y (L) value starts at 29 (starting value of buttons) and continues to go up by 12 each year.

By creating this X,Y table, you'll find that 8 years is when she will have finally collected at least 120 buttons. Below is an image of the graph to help elaborate further.

I hope this helps!

Answer 2

The answer to your question is k = 8, 9, 10, 11, ..........

Explanation:

Data

Number of buttons = 29

She collects 12 buttons every year

number of years she will have more than 120 buttons

Process

1.- Write an inequality to solve this problem

29 + 12k ≥ 120

2.- Solve for k

12k ≥ 120 - 29

12k ≥ 91

k ≥ 91/12

k ≥ 7.6

3.- Conclusion

k must be higher than 7.6 but look for whole numbers

k = 8, 9, 10, 11.......