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. The system of linear inequalities that describes the given information is y>120-1/2x (for 50% max heart rate) and y<165-3/4x (for 75%). A.Graph the system. Place a photo or link below to your graph.

Answer 1

We are given that:

x is the age, and

y is the heart rate

It is also given that $20\leq x\leq  65$

Now, we have been given that the person’s theoretical maximum heart rate (in heartbeats per minute) is $y=220 - x$ where x is the person’s age in years.

Therefore, 50% of $y=220 - x$ is $0.5(220-x)=110-0.5x$

Likewise, 75% of  $y=220 - x$ is $0.75(220-x)=165-0.75x$

Which is the same as The system of linear inequalities that describes the given information is y>120-1/2x (for 50% max heart rate) and y<165-3/4x (for 75%).

Thus, y will lie between these two extremes as:

$110-0.5x<y<165-0.75x$

The graph of the same is attached.