Question

in 4 and 5, complete the ratio tables to solve the problems.

1. apply math models every 5 days

during the week, morgan sleeps
40 hours. how many days would it
take him to sleep 200 hours?
morgans sleep ratio table
days
hours of
sleep

1. use patterns and structure alice

sleeps 50 hours every 6 days. does alice
or morgan have a greater days to hours
of sleep ratio? explain.
alices sleep ratio table
days
hours of
sleep

Explanation:

Step1: Find Morgan's sleep rate

First, calculate Morgan's daily sleep hours.
$\text{Daily sleep} = \frac{40}{5} = 8$ hours/day

Step2: Find days for 200 hours sleep

Divide total sleep by daily sleep hours.
$\text{Days} = \frac{200}{8} = 25$ days

Step3: Fill Morgan's ratio table

Scale the base 5 days/40 hours ratio:

• 5 days → 40 hours
• 10 days → $8 \times 10 = 80$ hours
• 15 days → $8 \times 15 = 120$ hours
• 20 days → $8 \times 20 = 160$ hours
• 25 days → $8 \times 25 = 200$ hours

Step4: Find Alice's sleep rate

Calculate Alice's daily sleep hours.
$\text{Daily sleep} = \frac{50}{6} \approx 8.33$ hours/day

Step5: Compare days-to-hours ratios

Morgan's ratio: $\frac{\text{Days}}{\text{Hours}} = \frac{5}{40} = \frac{1}{8}$
Alice's ratio: $\frac{\text{Days}}{\text{Hours}} = \frac{6}{50} = \frac{3}{25} = 0.12$, while $\frac{1}{8}=0.125$

Step6: Fill Alice's ratio table

Scale the base 6 days/50 hours ratio:

• 6 days → 50 hours
• 12 days → $50 \times 2 = 100$ hours
• 18 days → $50 \times 3 = 150$ hours
• 24 days → $50 \times 4 = 200$ hours
• 30 days → $50 \times 5 = 250$ hours

Answer:

Morgan's Sleep Ratio Table

Days	Hours of Sleep
10	80
15	120
20	160
25	200

Question 4 Answer:

25 days

Alice's Sleep Ratio Table

Days	Hours of Sleep
12	100
18	150
24	200
30	250

Question 5 Answer:

No, Morgan has a greater days-to-hours of sleep ratio. Morgan's ratio is $\frac{1}{8}=0.125$, while Alice's ratio is $\frac{3}{25}=0.12$, so Morgan's ratio is larger.