Question

for parts (a) and (b) below, choose the correct description. fill in the blanks as necessary.
(a)
a local store is keeping track of service times. the table below shows the number of customers served and the time it took.

number of customers	time (in minutes)
5	15
9	27

choose the correct description.

• it does not always take the same amount of time to serve each customer.
• it appears to take the same amount of time to serve each customer.

predicted amount of time to serve 10 customers: \\(\square\\) minutes

(b)
customers of a certain credit card earn points for using the card. the table below shows the number of points earned for the amount spent.

number of points	dollars spent
30	3
90	9

choose the correct description.

• each dollar spent does not always earn the same number of points.
• each dollar spent appears to earn the same number of points.

predicted amount spent to earn 100 points: \\(\\$\square\\)

Explanation:

Part (a)

Step 1: Determine time per customer

First, we find the time per customer for each entry. For 3 customers, time is 9 minutes, so per customer time is $\frac{9}{3} = 3$ minutes. For 5 customers, $\frac{15}{5} = 3$ minutes. For 9 customers, $\frac{27}{9} = 3$ minutes. So it takes 3 minutes per customer.

Step 2: Predict time for 10 customers

To find the time to serve 10 customers, we multiply the number of customers by the time per customer. So $10\times3 = 30$ minutes. Also, since the time per customer is constant (3 minutes), the correct description is "It appears to take the same amount of time to serve each customer."

Part (b)

Step 1: Determine points per dollar

First, find the points per dollar. For $2$ dollars, 20 points, so per dollar points is $\frac{20}{2} = 10$ points. For $3$ dollars, $\frac{30}{3} = 10$ points. For $9$ dollars, $\frac{90}{9} = 10$ points. So each dollar spent earns 10 points.

Step 2: Predict dollars for 100 points

To find the dollars needed to earn 100 points, we divide the number of points by points per dollar. So $\frac{100}{10} = 10$ dollars. Also, since points per dollar is constant (10 points per dollar), the correct description is "Each dollar spent appears to earn the same number of points."

Answer:

s:

Part (a)

• Predicted amount of time to serve 10 customers: $\boldsymbol{30}$ minutes
• Correct description: It appears to take the same amount of time to serve each customer.

Part (b)

• Predicted amount spent to earn 100 points: $\boldsymbol{10}$ dollars
• Correct description: Each dollar spent appears to earn the same number of points.