the problem is to use the information given to figure our who will win the third round of tugofwar.
round 1 on one side are four acrobats, each of equal strength. on the other side are five neighborhood grandmas, each of equal strength. the result is dead even.
round2 on one side is Ivan, a dog. Ivan is pitted against two of the grandmas andone acrobat. again it is a draw. no winner.
round 3 Ivan and three of the grandmas are on one side and the four acrobats are on the other.
Who will win the third round? Prove it!
Explain your thinking.
a = pull of acrobat
g = pull of grannies
then 5 g = 4 a
and g = 5/4 a
i = 2 g + a
so
i = 14/4 a = 7/2 a
i + 3 g vs 4 a
7/2 a + 15/4 a vs 4 a
29/4 a vs 4 a
29/4 a vs 16/4 a
check my arithmetic
Bigighkh
To determine who will win the third round of tug-of-war, we need to analyze the information given.
In round 1, there were four acrobats against five grandmas, and the result was a dead even draw. This suggests that each grandma and each acrobat have an equal amount of strength.
In round 2, Ivan, a dog, was pitted against two grandmas and one acrobat. Once again, the result was a draw. This implies that Ivan has the same amount of strength as two grandmas and one acrobat combined.
Now, in round 3, Ivan is joined by three grandmas, while the four acrobats remain on the other side. Since we know that each grandma has the same strength as one acrobat, this means that Ivan and the three grandmas have a combined strength equal to that of seven acrobats (4 acrobats on the opposing side + 3 grandmas).
Therefore, based on this analysis, the team consisting of Ivan and three grandmas will have more strength than the team of four acrobats. Therefore, Ivan and the grandmas will win the third round of tug-of-war.
To determine who will win the third round of tug-of-war, we need to analyze the given information and come to a conclusion based on the strength of each side. Let's break it down step by step:
In round 1:
- The four acrobats and five grandmas are evenly matched in terms of strength.
- This suggests that both teams are equally powerful.
In round 2:
- Ivan, the dog, is teamed up with two grandmas and one acrobat.
- This combination is still unable to defeat the remaining four acrobats.
- This implies that the four acrobats are collectively stronger or equal in strength to Ivan, two grandmas, and one acrobat.
Now, in round 3:
- Ivan and three grandmas are facing off against the four acrobats.
- Based on the information from round 2, we know that Ivan, two grandmas, and one acrobat were not enough to beat the four acrobats.
- Since the strength of Ivan, two grandmas, and one acrobat combined was not enough, adding one more grandma to their team will likely not be sufficient as well.
Therefore, the most logical conclusion is that the four acrobats will win the third round of tug-of-war. The cumulative strength of the acrobats appears to be greater than that of Ivan and the grandmas, based on the results of the previous rounds.
Proving this conclusion would require additional information or an explicit statement about the strength of each individual (such as the strength rankings of acrobats, grandmas, and Ivan). Without such information, this is the best inference based on the given data.