Question

Pam and Tommy collect geodes. Pam’s parents gave her 2 geodes to start her collection, and she buys 4 every year. Tommy has 2 geodes that were given to him for his birthday. He buys 4 every year. If Pam and Tommy continue to buy the same amount of geodes per year, when will Tommy have as many geodes as Pam? Explain your answer.

Answer 1

Pam and Tommy both start with 2 geodes and collect 4 additional geodes each year. Since their collection rates are the same, Tommy will always have the same number of geodes as Pam.

Step-by-step explanation:

The student's question is about comparing the growth of two geode collections over time. Both Pam and Tommy start with 2 geodes each and then add 4 geodes to their collection every year. We can write a simple equation to represent each person's collection as the years pass. Let's say y represents the number of years after they start collecting.

For Pam, the total number of geodes after y years would be 2 (the initial amount) plus 4 times y (the number of geodes bought each year), which gives us:

Pam's Geodes = 2 + 4y

For Tommy, the total number of geodes after y years is the same since he also collects 4 additional geodes per year:

Tommy's Geodes = 2 + 4y

As both equations are identical, we can see that the number of geodes they have will remain equal every year as long as they continue to collect the same number of geodes yearly. Thus, Tommy will always have as many geodes as Pam from the start, and this will continue as they add to their collections.