# Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.1 - Page 18: 129

a. The lower limit of the heart range, in beats per minute, for a 20-year-old with this exercise goal is 140 beats per minute. b.The upper limit of the heart range, in beats per minute, for a 20-year-old with this exercise goal is 160 beats per minute.

#### Work Step by Step

a. The lower limit uses the first formula. For age 20, substitute 20 for each "a" in the formula: $$H=\frac{7}{10}(220-a)$$ $$H=\frac{7}{10}(220-20)$$ $$H=\frac{7}{10}(200)$$ By writing the 200 as a fraction, you can cross reduce: $$H=\frac{7}{10}(\frac{200}{1})$$ $$H=\frac{7}{1}(\frac{20}{1})$$ $$H=7\times20$$ $$H=140$$ b. The upper limit uses the second formula. For age 20, substitute 20 for each "a" in the formula: $$H=\frac{4}{5}(220-a)$$ $$H=\frac{4}{5}(220-20)$$ $$H=\frac{4}{5}(200)$$ By writing the 200 as a fraction, you can cross reduce: $$H=\frac{4}{5}(\frac{200}{1})$$ $$H=\frac{4}{1}(\frac{40}{1})$$ $$H=4\times40$$ $$H=160$$

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