Final answer:
The student made a mistake in their initial calculation. Upon recalculating, the correct age for a person with a target heart rate of 133 beats per minute is 10 years old. For a 20-year-old person, the target heart rate at 70% intensity is 126 beats per minute.
Step-by-step explanation:
To solve part a), we will use the given equation y = 0.7(200 – x), where y is the target heart rate and x is the person’s age. Given that the target heart rate (y) is 133 beats per minute, we can set up the equation 133 = 0.7(200 – x) and solve for x.
133 = 0.7(200 – x)
140/0.7 = 200 – x
200 – (133 / 0.7) = x
200 – 190 = x
x = 10
So the person’s age would be 200 minus 10, which gives us 190 years old. However, this result is not possible as it exceeds the normal human lifespan and does not fit within the provided options A) 25 years old B) 30 years old C) 35 years old D) 40 years old. It seems there was a calculation error, let's redo the calculation with the correct arithmetic:
133 = 0.7(200 – x)
190 = 200 – x
x = 200 – 190
x = 10
The correct age of the person is 10 years old.
For part b), we simply need to substitute x with 20 to find the target heart rate for a 20-year-old person.
y = 0.7(200 – 20)
y = 0.7(180)
y = 126
Therefore, the target heart rate for a 20-year-old exercising at 70% intensity is 126 beats per minute.