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?

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Set up Inequalities: We need to set up two inequalities: one for the calls to Japan and one for the calls to Turkey. We know that Derin has a $25 calling card and the rates for calling Japan and Turkey are $0.19 per minute and $0.12 per minute, respectively. We also know that Derin wants to spend at least 30 minutes calling her family in Turkey.Call to Turkey Inequality: First, let's write the inequality for the calls to Turkey. Since Derin wants to spend at least 30 minutes calling Turkey, we can write this as T ≥ 30.Total Cost Inequality: Next, we need to consider the total cost of the calls to both Japan and Turkey. The total cost cannot exceed the $25 on the calling card. The cost for calling Japan is $0.19 per minute (J minutes), and the cost for calling Turkey is $0.12 per minute (T minutes). So, the inequality representing the total cost is 0.19J + 0.12T ≤ 25.System of Inequalities: Now we have the system of inequalities that represents the situation: 1. T ≥ 30 (Derin wants to spend at least 30 minutes calling Turkey) 2. 0.19J + 0.12T ≤ 25 (The total cost of calls to Japan and Turkey must not exceed $25)

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