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Dante commutes to work 44 mornings a week. For his commute each morning, he walks for 1010 minutes, waits and rides the bus for xx minutes, and waits and rides the train for yy minutes. If Dante spends at least 3.53.5 hours on his morning commute each week, which of the following inequalities best describes Dante's weekly morning commute?\newlineChoose 11 answer:\newline(A) x+y+10≥3.5(60)x+y+10 \geq 3.5(60)\newline(B) x+y+10≥3.5(60)(4)x+y+10 \geq 3.5(60)(4)\newline(C) 4(x+y)+10≥3.5(60)4(x+y)+10 \geq 3.5(60)\newline(D) 4(x+y+10)≥3.5(60)4(x+y+10) \geq 3.5(60)

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Q. Dante commutes to work 44 mornings a week. For his commute each morning, he walks for 1010 minutes, waits and rides the bus for xx minutes, and waits and rides the train for yy minutes. If Dante spends at least 3.53.5 hours on his morning commute each week, which of the following inequalities best describes Dante's weekly morning commute?\newlineChoose 11 answer:\newline(A) x+y+10≥3.5(60)x+y+10 \geq 3.5(60)\newline(B) x+y+10≥3.5(60)(4)x+y+10 \geq 3.5(60)(4)\newline(C) 4(x+y)+10≥3.5(60)4(x+y)+10 \geq 3.5(60)\newline(D) 4(x+y+10)≥3.5(60)4(x+y+10) \geq 3.5(60)
  1. Rephrasing the problem: Let's first rephrase the ＂What inequality best describes Dante's weekly morning commute time in minutes if he commutes 44 mornings a week and spends at least 3.53.5 hours on his commute?＂
  2. Breakdown of Dante's weekly commute: Dante's weekly commute consists of walking, waiting and riding the bus, and waiting and riding the train. Each morning, this amounts to 1010 minutes of walking, xx minutes on the bus, and yy minutes on the train. Since he commutes 44 mornings a week, we need to multiply the daily times by 44 to get the weekly times.
  3. Calculating the total weekly commute time: The total time spent commuting each morning is the sum of the walking time, bus time, and train time, which is 10+x+y10 + x + y minutes. Over the course of a week, this becomes 4(10+x+y)4(10 + x + y) minutes.
  4. Converting hours to minutes: Dante spends at least 3.53.5 hours on his commute each week. To compare this with his commute time in minutes, we need to convert 3.53.5 hours into minutes. Since 11 hour is 6060 minutes, 3.53.5 hours is 3.5×603.5 \times 60 minutes.
  5. Setting up the inequality: Now we can set up the inequality. Dante's total weekly commute time in minutes must be greater than or equal to 3.53.5 hours in minutes. This gives us the inequality 4(10+x+y)≥3.5×604(10 + x + y) \geq 3.5 \times 60.
  6. Simplifying the inequality: Simplifying the inequality, we get 4(10+x+y)≥2104(10 + x + y) \geq 210. This matches one of the answer choices provided.

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