Tommy is going to be participating in a long bike race soon. He needs to ride a total of at least 119 kilometers today. He plans to do this by riding multiple laps on the Highland Loop, which is 17 kilometers long, and the Pinehurst Loop, which is 49 kilometers long. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. x = the number of laps on the Highland Loop y = the number of laps on the Pinehurst Loop Choices: (A)17x + 49y 119 (B)49x + 17y ≥ 119 (C)49x + 17y 119 (D)17x + 49y ≥ 119

Question

Tommy is going to be participating in a long bike race soon. He needs to ride a total of at least 119 kilometers today. He plans to do this by riding multiple laps on the Highland Loop, which is 17 kilometers long, and the Pinehurst Loop, which is 49 kilometers long.  Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. x = the number of laps on the Highland Loop y = the number of laps on the Pinehurst Loop     Choices: (A)17x + 49y > 119 (B)49x + 17y ≥ 119 (C)49x + 17y > 119 (D)17x + 49y ≥ 119

Bytelearn · Accepted Answer

Identify Required Distance: Tommy needs to ride at least 119 kilometers, so we're looking for an inequality that represents this. The Highland Loop is 17 kilometers long, and the Pinehurst Loop is 49 kilometers long. If x is the number of laps on the Highland Loop and y is the number of laps on the Pinehurst Loop, then the total distance Tommy rides is 17x + 49y. Since he needs to ride at least 119 kilometers, the inequality should reflect that the total distance is greater than or equal to 119. Formulate Inequality: We write the inequality as 17x + 49y ≥ 119, because Tommy can ride exactly 119 kilometers or more. This inequality shows that the total distance covered by riding x laps of the Highland Loop and y laps of the Pinehurst Loop should be at least 119 kilometers. Check Given Choices: Now we check the choices given to see which one matches our inequality. Choice (A) says 17x + 49y > 119, but this means Tommy would have to ride more than 119 kilometers, which is not what's required; he just needs to ride at least 119 kilometers. Choice (B) says 49x + 17y ≥ 119, but this has the coefficients for x and y swapped. Choice (C) says 49x + 17y > 119, which also has the coefficients swapped and indicates more than 119 kilometers. Choice (D) says 17x + 49y ≥ 119, which matches our inequality exactly.

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