Questions: (a) Raisel is deciding how many people to take on the movies. The table below shows the cost for different sized groups of people. Number in group Cost (in dollars) 3 24 4 30 9 45 15 20 One cost for each person is not always the same. (b) A train travels from City A to City B. The table below shows the distance and time it takes on the train. Distance (km) Time (in minutes) 8 15 15 18 2 5 6 6

(a) Raisel is deciding how many people to take on the movies. The table below shows the cost for different sized groups of people. Number in group Cost (in dollars) 3 24 4 30 9 45 15 20 One cost for each person is not always the same. (b) A train travels from City A to City B. The table below shows the distance and time it takes on the train. Distance (km) Time (in minutes) 8 15 15 18 2 5 6 6
Transcript text: (a) Raisel is deciding how many people to take on the movies. The table below shows the cost for different sized groups of people. Number in group | Cost (in dollars) 3 | 24 4 | 30 9 | 45 15 | 20 One cost for each person is not always the same. (b) A train travels from City A to City B. The table below shows the distance and time it takes on the train. Distance (km) | Time (in minutes) 8 | 15 15 | 18 2 | 5 6 | 6
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Solution

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Solution Steps

Step 1: Analyze the cost per person for each group size in part (a)
  • For 3 people: Cost per person = \( \frac{24}{3} = 8 \) dollars.
  • For 4 people: Cost per person = \( \frac{30}{4} = 7.5 \) dollars.
  • For 9 people: Cost per person = \( \frac{45}{9} = 5 \) dollars.
  • For 15 people: Cost per person = \( \frac{20}{15} \approx 1.33 \) dollars.
Step 2: Identify the most cost-effective group size in part (a)
  • The cost per person decreases as the group size increases. The smallest cost per person is for the group of 15 people, at approximately \( 1.33 \) dollars per person.
Step 3: Calculate the speed of the train for each distance and time in part (b)
  • For 8 km in 15 minutes: Speed = \( \frac{8}{15} \times 60 = 32 \) km/h.
  • For 15 km in 18 minutes: Speed = \( \frac{15}{18} \times 60 = 50 \) km/h.
  • For 2 km in 5 minutes: Speed = \( \frac{2}{5} \times 60 = 24 \) km/h.
  • For 6 km in 6 minutes: Speed = \( \frac{6}{6} \times 60 = 60 \) km/h.

Final Answer

(a) The most cost-effective group size is \( \boxed{15} \) people.
(b) The speeds for the distances are \( \boxed{32} \) km/h, \( \boxed{50} \) km/h, \( \boxed{24} \) km/h, and \( \boxed{60} \) km/h respectively.

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