Maria shares some seashells with Jeff.

Maria says, “Two for you, three for me, two for you, three for me ...”
Tonya watches.
At the end, she says, “So Jeff got 2 of the shells.”
3
Do you agree with Tonya? Give reasons for your answer.

1 answer

To understand whether Tonya is correct in her claim that Jeff received 2 seashells, let's analyze the sharing process as described by Maria.

From Maria's statement, she shares seashells in a repeating pattern: "two for you, three for me." This means that each cycle of sharing consists of:

  • 2 seashells for Jeff
  • 3 seashells for Maria

We can summarize this as one complete cycle giving a total of 5 seashells shared: 2 to Jeff and 3 to Maria.

If we repeat this cycle:

  • In the first complete cycle: Jeff gets 2 seashells.
  • In the second complete cycle: Jeff gets another 2 seashells.

If the sharing continues for any number of complete cycles, Jeff will receive 2 seashells for each cycle.

If we assume that they carry out multiple cycles, let's say they do it \( n \) times:

  • Jeff would end up with \( 2n \) seashells.

Without more specific information about how many complete cycles they executed, we cannot definitively state how many seashells Jeff received. However, the claim that Jeff only got 2 seashells holds true only if Maria stopped after the first cycle.

Therefore, if the sharing went on for more than one cycle, Tonya's statement that "Jeff got 2 of the shells" could potentially be incorrect. It all depends on how many rounds of sharing Maria and Jeff completed.

In summary:

  • If only one cycle was completed, then Tonya is correct: Jeff received 2 seashells.
  • If multiple cycles occurred, Jeff would have received more than 2 shells, which means Tonya would not be correct.

Without knowing the exact number of cycles, we cannot definitively agree with Tonya.