Question

problems 5–7: han and priya are at swim practice. for every 3 strokes priya takes, han takes 5 strokes. suppose x represents the number of strokes priya takes and y represents the number of strokes han takes. 5. complete the table.
number of priya’s strokes (x) | 24 | 36 | 75
number of han’s strokes (y) | | |

Explanation:

Step1: Find the ratio

For every 3 strokes Priya takes, Han takes 5 strokes. So the ratio of Han's strokes to Priya's strokes is \( \frac{5}{3} \). So \( y=\frac{5}{3}x \).

Step2: Calculate for \( x = 24 \)

Substitute \( x = 24 \) into \( y=\frac{5}{3}x \). \( y=\frac{5}{3}\times24 = 5\times8 = 40 \).

Step3: Calculate for \( x = 36 \)

Substitute \( x = 36 \) into \( y=\frac{5}{3}x \). \( y=\frac{5}{3}\times36 = 5\times12 = 60 \).

Step4: Calculate for \( x = 75 \)

Substitute \( x = 75 \) into \( y=\frac{5}{3}x \). \( y=\frac{5}{3}\times75 = 5\times25 = 125 \).

Answer:

For \( x = 24 \), \( y = 40 \); for \( x = 36 \), \( y = 60 \); for \( x = 75 \), \( y = 125 \)