Question

A person’s theoretical maximum heart rate (in heartbeats per minute) is 220 - x where x is the person’s age in years (20 ≤ x ≤ 65). When a person exercises, it is recommended that the person strive for a heart rate that is at least 50% of the maximum and at most 75% of the maximum.

Write a system of linear inequalities that describes the given information.

Answer 1

Let f(x) represents the heart beat of the person.

Now, we have been given that person’s theoretical maximum heart rate is given by  220 - x.

Also, we have been given that person strive for a heart rate that is at least 50% of the maximum. At least means greater than equal to.

Thus, we have

$f(x)\geq (220-x)0.5\\ f(x)\geq 110-0.5x$

Also, we have been given that person strive for a heart rate that is at most 75% of the maximum. At most means less than equal to.

$f(x)\leq (220-x)0.75\\ \\ f(x)\leq 165-0.75x$

Therefore, the system of inequality is given by

$f(x)\geq 110-0.5x\\ f(x)\leq 165-0.75x$