Question

someones heartrate
minutes | beats
1 | x
3 | 165
y | 385

Explanation:

To solve for \( x \) (beats per minute) and \( y \) (minutes for 385 beats), we can use the concept of proportionality since heart rate is constant (beats per minute is constant).

Step 1: Find the heart rate \( x \) (beats per minute)

We know that in 3 minutes, there are 165 beats. The heart rate \( x \) (beats per minute) can be found by dividing the number of beats by the number of minutes.

$$ x=\frac{165}{3} $$

$$ x = 55 $$

So, the heart rate is 55 beats per minute.

Step 2: Find the time \( y \) (in minutes) for 385 beats

Since the heart rate is constant (55 beats per minute), we can set up a proportion. Let \( y \) be the number of minutes for 385 beats. The heart rate is \( \frac{\text{beats}}{\text{minutes}} \), so:

$$ \frac{385}{y}=55 $$

To solve for \( y \), we can cross - multiply:

$$ 55y = 385 $$

Then divide both sides by 55:

$$ y=\frac{385}{55} $$

$$ y = 7 $$

Answer:

The value of \( x \) is 55 (beats per minute) and the value of \( y \) is 7 (minutes). If we were just asked for \( x \), the answer is 55; if just for \( y \), the answer is 7. If for both, \( x = 55,y = 7\).