Ni Hua 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

Ni Hua 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

Denote Islands and Peninsulas:  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. The total number of skydives is 45, and the total number of places (islands and peninsulas) visited is 19. We can set up two equations based on this information. Equation for Skydives:  The first equation represents the total number of skydives: $2I + 3P = 45$. This equation comes from the fact that Ni Hua skydives twice on each island ($2I$) and thrice on each peninsula ($3P$), totaling 45 skydives. Equation for Places Visited:  The second equation represents the total number of places visited: $I + P = 19$. This equation simply adds the number of islands ($I$) and the number of peninsulas ($P$) to get the total number of places visited, which is 19. Substitute and Solve:  To solve this system of equations, we can use substitution or elimination. Let's use substitution. We can solve the second equation for $I$: $I = 19 - P$. This equation isolates $I$ in terms of $P$, making it easier to substitute into the first equation. Simplify and Solve:  Substitute $I = 19 - P$ into the first equation: $2(19 - P) + 3P = 45$. This substitution will allow us to solve for $P$. Calculate Peninsulas:  Simplify and solve for $P$: $38 - 2P + 3P = 45$. Combine like terms to get $38 + P = 45$. Then, subtract 38 from both sides to isolate $P$: $P = 45 - 38$. Substitute for Islands:  Calculate $P$: $P = 7$. This means Ni Hua visited 7 peninsulas. Calculate Islands:  Now, substitute $P = 7$ back into the equation $I = 19 - P$ to find $I$: $I = 19 - 7$. Final Answer:  Calculate $I$: $I = 12$. This means Ni Hua visited 12 islands.  We have found that Ni Hua visited 12 islands and 7 peninsulas. This matches option (A) in the given choices.

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