When Famke charges her phone, it gains 2 percentage points each minute. When Famke uses her phone, it loses 5 percentage points each minute. Once, Famke used her phone for some time, and then charged it for twice the amount of time she used it. In the end, her phone lost 10 percentage points. How long did Famke use her phone and how long did she charge it? Choose 1 answer: (A) There is not enough information to determine the exact time Famke used and charged her phone. (B) The given information describes an impossible situation. (C) Famke used her phone for 10 minutes, and charged her phone for 20 minutes. (D) Famke used her phone for 20 minutes, and charged her phone for 10 minutes.

Question

When Famke charges her phone, it gains 2 percentage points each minute. When Famke uses her phone, it loses 5 percentage points each minute. Once, Famke used her phone for some time, and then charged it for twice the amount of time she used it. In the end, her phone lost 10 percentage points. How long did Famke use her phone and how long did she charge it? Choose 1 answer: (A) There is not enough information to determine the exact time Famke used and charged her phone. (B) The given information describes an impossible situation. (C) Famke used her phone for 10 minutes, and charged her phone for 20 minutes. (D) Famke used her phone for 20 minutes, and charged her phone for  10 minutes.

Bytelearn · Accepted Answer

Denote Time Used: Let's denote the time Famke used her phone as $ t $ minutes. According to the problem, she charged her phone for twice the amount of time she used it, which means she charged it for $ 2t $ minutes.Calculate Net Change: Now, let's calculate the net change in the battery percentage. When Famke uses her phone, it loses 5 percentage points each minute, so after $ t $ minutes, the total loss is $ 5t $ percentage points. When she charges her phone, it gains 2 percentage points each minute, so after $ 2t $ minutes, the total gain is $ 4t $ percentage points (since $ 2 \times 2t = 4t $).Set Up Equation: The net change in the battery percentage is the gain from charging minus the loss from using the phone. The problem states that the net change is a loss of 10 percentage points. Therefore, we can set up the following equation: Net change = Gain from charging - Loss from using -10 = 4t - 5tSolve for Time: Solving the equation for $ t $: -10 = 4t - 5t -10 = -t t = 10Calculate Total Time: Since $ t $ is the time Famke used her phone, she used it for 10 minutes. She charged her phone for twice that time, which means she charged it for $ 2t $ minutes, or $ 2 \times 10 = 20 $ minutes.

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