The expression on the left-hand side of the inequality represents the minimum while the expression on the right-hand side represents the maximum.
A
a
102.5≤ R ≤ 184.5.
B
b
22 years old
Practice makes perfect
a
We can use the given inequality to determine corresponding ages and heart rate ranges. We are given an age of 15 years so we simply substitute a=15 into the inequality and solve for the corresponding heart rate, R.
The solution 102.5 ≤ R ≤ 184.5 means that for a person who is 15 years old, the recommended heart rate is between 102.5 and 184.5.
b
Because the given inequality is a compound inequality, the left side represents the lower bound or minimum value, while the right side represents the upper bound or maximum value. Pulling apart the inequality we get two inequalities:
minimum value:& 0.5(220-a) ≤ R
maximum value:& R ≤ 0.9(220-a)
We are asked to solve for a when R is between 99 and 178.2. This means the minimum value is 99 and the maximum is 178.2. To solve for a, we can substitute 99 into the first inequality and 178.2 into the second one, and solve for a in each of them.
The solution a ≥ 22 means that with a recommended minimum heart rate of 99, the person should be 22 years old or older. We will now solve Inequality 2.
The solution a ≤ 22 means that with a recommended maximum heartrate of 178.2, the person should be 22 years old or younger. Combining the solutions from both inequalities we have
a ≥ 22 and a ≤ 22.
The overlap between these is a=22. Thus, the age of a person with a target heartrate of 99 to 178.2 is 22 years old.
