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Derin is travelling abroad with a $25 calling card. The rate to call her boyfriend in Japan is $0.19 per minute. The rate to call her family in Turkey is $0.12 per minute. Derin wants to spend at least 30 minutes calling her family in Turkey. Which of the following systems of inequalities best represents the relationship between J, the number of minutes Derin calls Japan, and T, the number of minutes Derin calls Turkey? Choose 1 answer: (A) 0.19 J+0.12 T <= 25 T <= 30 (D) 0.19 J+0.12 T >= 25 T <= 30 (C) 0.19 J+0.12 T <= 25 T >= 30 (D) 0.19 J+0.12 T >= 25 T > 30

Derin is travelling abroad with a $25\$25 calling card. The rate to call her boyfriend in Japan is $0.19\$0.19 per minute. The rate to call her family in Turkey is $0.12\$0.12 per minute. Derin wants to spend at least 3030 minutes calling her family in Turkey. Which of the following systems of inequalities best represents the relationship between JJ, the number of minutes Derin calls Japan, and TT, the number of minutes Derin calls Turkey?\newlineChoose 11 answer:\newlineAA 0.19J+0.12T≤250.19J+0.12T \leq 25\newlineT≤30T \leq 30\newlineBB 0.19J+0.12T≥250.19J+0.12T \geq 25\newlineT≤30T \leq 30\newlineCC 0.19J+0.12T≤250.19J+0.12T \leq 25\newlineT≥30T \geq 30\newlineDD \newline0.19J+0.12T≥250.19J+0.12T \geq 25\newlineT > 30

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Full solution

Q. Derin is travelling abroad with a $25\$25 calling card. The rate to call her boyfriend in Japan is $0.19\$0.19 per minute. The rate to call her family in Turkey is $0.12\$0.12 per minute. Derin wants to spend at least 3030 minutes calling her family in Turkey. Which of the following systems of inequalities best represents the relationship between JJ, the number of minutes Derin calls Japan, and TT, the number of minutes Derin calls Turkey?\newlineChoose 11 answer:\newlineAA 0.19J+0.12T≤250.19J+0.12T \leq 25\newlineT≤30T \leq 30\newlineBB 0.19J+0.12T≥250.19J+0.12T \geq 25\newlineT≤30T \leq 30\newlineCC 0.19J+0.12T≤250.19J+0.12T \leq 25\newlineT≥30T \geq 30\newlineDD \newline0.19J+0.12T≥250.19J+0.12T \geq 25\newlineT>30T > 30
  1. Total Cost Inequality: Derin has a $25\$25 calling card and wants to spend at least 3030 minutes calling her family in Turkey. The cost per minute for calling Turkey is $0.12\$0.12, and the cost per minute for calling Japan is $0.19\$0.19. We need to find the system of inequalities that represents the total cost of calls to Japan and Turkey without exceeding the $25\$25 on the calling card and ensuring that the time spent calling Turkey is at least 3030 minutes.
  2. Minimum Time Inequality: First, let's write an inequality for the total cost of the calls. The total cost is the sum of the cost of calls to Japan and the cost of calls to Turkey, which must be less than or equal to $25\$25. This can be represented by the inequality:\newline0.19J+0.12T≤250.19J + 0.12T \leq 25
  3. Combined System of Inequalities: Next, we need to represent the condition that Derin wants to spend at least 3030 minutes calling her family in Turkey. This can be represented by the inequality:\newlineT≥30T \geq 30
  4. Combined System of Inequalities: Next, we need to represent the condition that Derin wants to spend at least 3030 minutes calling her family in Turkey. This can be represented by the inequality:\newlineT≥30T \geq 30Combining the two inequalities, we get the system:\newline0.19J+0.12T≤250.19J + 0.12T \leq 25\newlineT≥30T \geq 30\newlineThis system of inequalities satisfies both conditions: the total cost does not exceed $25\$25, and the time spent calling Turkey is at least 3030 minutes.

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