Question

for parts (a) and (b) below, choose the correct description. fill in the blanks as necessary.
(a) trey is deciding how many people to take to the movies. the table below shows the cost for different sized groups of people.

number in group	2	5	6

choose the correct description.
○ the cost for each person is not always the same.
○ the cost for each person appears to be the same.
predicted number in group for a cost of $56:
(b) a train travels from city a to city b. the table below shows the distance and the amount of time it takes on the train.

distance (in kilometers)	12	24	42

choose the correct description.
○ the train does not always go the same distance each minute.
○ the train appears to go the same distance each minute.
predicted distance traveled in 9 minutes: km

Explanation:

Part (a)

Step1: Calculate cost per person for each group

For group of 2: $\frac{16}{2} = 8$ dollars per person.
For group of 5: $\frac{35}{5} = 7$ dollars per person.
For group of 6: $\frac{42}{6} = 7$ dollars per person.
Since the cost per person is not consistent (8 vs. 7), the first option is correct.

Step2: Predict number in group for $56

If we assume the cost per person is 7 (from groups of 5 and 6), then number of people = $\frac{56}{7} = 8$.

Part (b)

Step1: Calculate distance per minute for each case

For 12 km in 2 min: $\frac{12}{2} = 6$ km per minute.
For 24 km in 4 min: $\frac{24}{4} = 6$ km per minute.
For 42 km in 7 min: $\frac{42}{7} = 6$ km per minute.
Since distance per minute is consistent (6 km/min), the second option is correct.

Step2: Predict distance in 9 minutes

Distance = speed × time = $6 \times 9 = 54$ km.

Answer:

(a) The cost for each person is not always the same.
Predicted number in group for a cost of $56: 8

(b) The train appears to go the same distance each minute.
Predicted distance traveled in 9 minutes: 54 km