NiHua is an adventurous traveler. He skydives twice in every island he visits and skydives thrice in every peninsula he visits. In the last decade, Ni Hua went skydiving a total of 45 times in the 19 islands and peninsulas that he visited. How many islands and peninsulas did Ni Hua visit? Choose 1 answer: (A) Ni Hua visited 12 islands and 7 peninsulas. (B) Ni Hua visited 7 islands and 12 peninsulas. (c) There is not enough information to determine the exact number of islands and peninsula Ni Hua visited. (D) The given information describes an impossible situation.

Question

NiHua is an adventurous traveler. He skydives twice in every island he visits and skydives thrice in every peninsula he visits. In the last decade, Ni Hua went skydiving a total of 45 times in the 19 islands and peninsulas that he visited. How many islands and peninsulas did Ni Hua visit? Choose 1 answer: (A) Ni Hua visited 12 islands and 7 peninsulas. (B) Ni Hua visited 7 islands and 12 peninsulas. (c) There is not enough information to determine the exact number of islands and peninsula  Ni Hua visited. (D) The given information describes an impossible situation.

Bytelearn · Accepted Answer

Define Variables: Let's denote the number of islands Ni Hua visited as i and the number of peninsulas as p. We know that Ni Hua skydives twice on each island and thrice on each peninsula. We also know that he visited a total of 19 islands and peninsulas and went skydiving 45 times. We can set up the following system of equations: 1. 2i + 3p = 45 (total number of skydives) 2. i + p = 19 (total number of places visited)Set Up Equations: We can solve this system of equations using substitution or elimination. Let's use substitution. From the second equation, we can express i in terms of p: i = 19 - p.Substitute and Solve: Substitute i = 19 - p into the first equation: 2(19 - p) + 3p = 45.Distribute and Combine: Now, let's solve for p. First, distribute the 2: 38 - 2p + 3p = 45.Isolate p: Combine like terms: 38 + p = 45.Calculate p: Subtract 38 from both sides to isolate p: p = 45 - 38.Find i: Calculate the value of p: p = 7.Calculate i: Now that we have the value of p, we can find i using the equation i = 19 - p: i = 19 - 7.Final Answer: Calculate the value of i: i = 12.We have found that Ni Hua visited 12 islands and 7 peninsulas. This corresponds to option (A).

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