Question

When exercising, a person's pulse rate should not exceed a certain limit. This maximum rate is represented by the expression $0.8(220-a),$ where a is age in years. Find the age of a person whose maximum pulse rate is 152

Short answer

The age of a person whose maximum pulse rate is 152 is at least 30 years.

Step-by-step solution

Step 1. Use the definition of inequality expression.

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

Step 2. Set up an equation.

Since age cannot exceed 152 we have the inequation

$0.8\left(220-a\right)\le 152$

Step 3. Solve possible solutions.

We have obtained the expressions: $0.8\left(220-a\right)\le 152$, we solve this inequality as shown:

role="math" localid="1642665923184" $\begin{array}{l}0.8\left(220-a\right)\le 152\\ 220-a\le \frac{152}{0.8}\text{[Divideby0.8bothsides]}\\ 220-a\le 190\\ 220-a-220\le 190-220\text{[add-220bothsides]}\\ -a\le -30\\ -a\times \left(-1\right)\le -30\times \left(-1\right)\text{[multiplybothsidesby-1andflipthesigninnextstep]}\\ a\ge 30\end{array}$

The age of a person whose maximum pulse rate is 152 is thus at least 30 years.