Question

Please help!!! I've been trying to figure this out all day!

The American College of Sports Medicine considers age as one factor when it recommends low and
high heart rates during workout sessions.
For safe and efficient exercise, your heart rate should be between 55% and 90% of the maximum
heart rate level. The maximum heart rate is calculated by subtracting a person's age from 220
beats per minute.
(Let a represent a person's age and h represent the person's recommended heart rate.)
1. The following equation represents the low value for heart rate. Simplify the equation.
h = .55(220-a)
2. The following equation represents the high value for heart rate. Simplify the equation.
h = .90(220-a)
3. Use these two expressions to write a system of inequalities that represents the heart rate range
for safe and efficient exercise. (Hint: you need to write two separate inequalities)

Answer 1

To simplify the equations, distribute the coefficients, then write two inequalities using the simplified equations.

Step-by-step explanation:

1. To simplify the equation for the low value of heart rate, we can distribute the 0.55 to remove the parentheses: h = 0.55 * 220 - 0.55a. Multiplying 0.55 by 220 gives us 121, so the equation simplifies to h = 121 - 0.55a.

2. Similarly, we can simplify the equation for the high value of heart rate by distributing the 0.9: h = 0.9 * 220 - 0.9a. Multiplying 0.9 by 220 gives us 198, so the equation simplifies to h = 198 - 0.9a.

3. To write a system of inequalities that represents the heart rate range for safe and efficient exercise, we can use the simplified equations from step 1 and step 2. The inequalities are: h >= 121 - 0.55a and h <= 198 - 0.9a.

Answer 2

.55(220-a) + .90(220-a)

Step-by-step explanation: