Marcel plugged in his work tablet and phone. The phone had a battery charge of 13% and started increasing by 2 percentage points every 3 minutes. The tablet had charge of 25% and started increasing by 1 percentage point every 3 minutes. Let t represent the time, in minutes, since Marcel plugged in the phone and tablet. Complete the inequality to represent the times when the phone would have at least as much battery charge as the tablet. t select inequality symbol □ minutes

Question

Marcel plugged in his work tablet and phone. The phone had a battery charge of  13% and started increasing by 2 percentage points every 3 minutes. The tablet had charge of  25% and started increasing by 1 percentage point every 3 minutes. Let  t represent the time, in minutes, since Marcel plugged in the phone and tablet. Complete the inequality to represent the times when the phone would have at least as much battery charge as the tablet.  t select inequality symbol □ minutes

Bytelearn · Accepted Answer

Define phone charge function: Let's define the battery charge of the phone as a function of time, t. The phone starts with a 13% charge and increases by 2 percentage points every 3 minutes. So, the charge of the phone after t minutes can be represented as: Phone charge = 13 + (2/3)tDefine tablet charge function: Similarly, we can define the battery charge of the tablet as a function of time, t. The tablet starts with a 25% charge and increases by 1 percentage point every 3 minutes. So, the charge of the tablet after t minutes can be represented as: Tablet charge = 25 + (1/3)tSet up inequality: We need to find when the phone's charge is at least as much as the tablet's charge. This means we are looking for the time t when the phone's charge is greater than or equal to the tablet's charge. So, we set up the inequality: 13 + (2/3)t ≥ 25 + (1/3)tEliminate fractions: To solve the inequality, we will first eliminate the fractions by multiplying every term by 3 to get rid of the denominators: 3 * (13 + (2/3)t) ≥ 3 * (25 + (1/3)t) This simplifies to: 39 + 2t ≥ 75 + tIsolate variable: Next, we will isolate t on one side of the inequality by subtracting t from both sides: 39 + 2t - t ≥ 75 + t - t This simplifies to: 39 + t ≥ 75Solve for t: Now, we subtract 39 from both sides to solve for t: 39 + t - 39 ≥ 75 - 39 This simplifies to: t ≥ 36Final result: The inequality t ≥ 36 represents the times when the phone would have at least as much battery charge as the tablet.

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