Derin's 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) 0.19J+0.12T≤25T≤30(B) 0.19J+0.12T≥25T≤30(C) 0.19J+0.12T≤25T≥30(D) 0.19J+0.12T≥25T≥30
Q. Derin's 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) 0.19J+0.12T≤25T≤30(B) 0.19J+0.12T≥25T≤30(C) 0.19J+0.12T≤25T≥30(D) 0.19J+0.12T≥25T≥30
Set Up Inequalities: We need to set up two inequalities: one to represent the cost of the calls and another to represent the time spent calling Turkey.
Total Cost Inequality: The first inequality will represent the total cost of the calls to Japan and Turkey. We don't know the exact amount Derin wants to spend, but we know it should be at least $25 based on the options given. Therefore, the inequality will either be greater than or equal to 25 (≥25) or less than or equal to25 (≤25).
Time Spent Inequality: The second inequality will represent the time Derin wants to spend calling Turkey. We know that Derin wants to spend at least 30 minutes calling Turkey, so the inequality will be greater than or equal to 30 (T≥30).
Determine Cost Inequality: Now we need to determine whether the cost inequality should be greater than or equal to 25 or less than or equal to 25. Since the problem states that Derin wants to spend "at least" 30 minutes calling Turkey, it implies that she has a minimum budget she is willing to spend. Therefore, the cost inequality should be greater than or equal to 25 (≥25).
Combine Inequalities: Combining the two inequalities, we get the system:0.19J+0.12T≥25 (for the cost)T≥30 (for the time calling Turkey)
Match Answer Choice: Looking at the answer choices, we see that option (D) matches our system of inequalities:(D) 0.19J+0.12T≥25T≥30
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