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Algebra / Linear inequalities in one or two variables Difficulty: Medium

$H equals, 120 p, plus 60$

The Karvonen formula above shows the relationship between Alice’s target heart rate H, in beats per minute (bpm), and the intensity level p of different activities. When $p equals 0$ , Alice has a resting heart rate. When $p equals 1$ , Alice has her maximum heart rate. It is recommended that p be between 0.5 and 0.85 for Alice when she trains. Which of the following inequalities describes Alice’s target training heart rate?

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Explanation

Choice A is correct. When Alice trains, it’s recommended that p be between 0.5 and 0.85. Therefore, her target training heart rate is represented by the values of H corresponding to $0 point 5 is less than or equal to p, which is less than or equal to 0 point 8 5$ . When $p equals 0 point 5$ , $H equals, 120 times 0 point 5, plus 60$ , or $H equals 120$ . When $p equals 0 point 8 5$ , $H equals, 120 times 0 point 8 5, plus, 60$ , or $H equals 162$ . Therefore, the inequality that describes Alice’s target training heart rate is $120 is less than or equal to H, which is less than or equal to 162$ .

Choice B is incorrect. This inequality describes Alice’s target heart rate for $0 point 3 5 is less than or equal to p, which is less than or equal to 0 point 5$ . Choice C is incorrect. This inequality describes her target heart rate for $0 is less than or equal to p, which is less than or equal to 0 point 8 5$ . Choice D is incorrect. This inequality describes her target heart rate for $0 is less than or equal to p, which is less than or equal to 0 point 3 5$ .