Answer
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: $$H=\frac{4}{5}(\frac{200}{1})$$ $$H=\frac{4}{1}(\frac{40}{1})$$ $$H=4\times40$$ $$H=160$$
