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5.1 Linear Inequalities in One or Two Variables - Compound inequalities
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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?

A.

120 is less than or equal to H, which is less than or equal to 162

B.

102 is less than or equal to H, which is less than or equal to 120

C.

60 is less than or equal to H, which is less than or equal to 162

D.

60 is less than or equal to H, which is less than or equal to 102

The Karvonen formula above shows the relationship between Alice’s target heart rate H , in beats

Hard-difficulty · SAT Math · Linear Inequalities in One or Two Variables — Compound inequalities. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer 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.

 

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