Question

housekeeping staff at the weary traveler hotel rotates job assignments every today, martha is in charge of folding the freshly cleaned bedsheets. there is a proportional relationship between the amount of time (in minutes) martha spends folding, x, and the number of bedsheets she folds, y. x (minutes) | y (bedsheets) 10 | 60 13 | 78 14 | 84 15 | 90 write an equation for the relationship between x and y. simplify any fractions. y = 9. carrie uses her phone primarily to take a lot of selfies. the storage space on her phone is limited, so carrie needs to keep track of how many selfies she takes. there is a proportional relationship between the number of selfies carrie takes, x, and the amount of storage (in megabytes) she uses taking selfies, y. x (selfies) | y (megabytes) 10 | 20 12 | 24 21 | 42 22 | 44 write an equation for the relationship between x and y. simplify any fractions. y =

Explanation:

First Problem (Martha's Bedsheets)

Step1: Recall proportional relationship

For a proportional relationship, \( y = kx \), where \( k \) is the constant of proportionality. To find \( k \), use \( k=\frac{y}{x} \).
Take the first pair \((x = 10, y = 60)\). Then \( k=\frac{60}{10}=6 \).

Step2: Verify with other pairs

Check \((13, 78)\): \( \frac{78}{13}=6 \). Check \((14, 84)\): \( \frac{84}{14}=6 \). Check \((15, 90)\): \( \frac{90}{15}=6 \). So \( k = 6 \).

Step1: Recall proportional relationship

For proportional \( y = kx \), find \( k=\frac{y}{x} \). Take first pair \((x = 10, y = 20)\). Then \( k=\frac{20}{10}=2 \).

Step2: Verify with other pairs

Check \((12, 24)\): \( \frac{24}{12}=2 \). Check \((21, 42)\): \( \frac{42}{21}=2 \). Check \((22, 44)\): \( \frac{44}{22}=2 \). So \( k = 2 \).

Answer:

\( y = 6x \)

Second Problem (Carrie's Selfies)