Question

4. A department store offers a rewards card for frequent customers. Every time a customer earns 100

or more points, the customer receives a gift certificate. Each purchase is worth 12 points, and customers
automatically earn 25 points when they sign up. Which inequalities could be solved to find the number of
purchases, p, that a customer needs to make in order to earn the first gift certificate? Select all the correct
answers.
A) 12p+ 25 <100
B) 12p+252 100
C) 12p+ 25 100
5. A table of values is shown below.
D) 12p-25 ≥100
E) 25 > 100-12p
F) 12p≥ 100-25

Answer 1

The correct inequalities that could be solved to find the number of purchases that a customer needs to make in order to earn the first gift certificate are:

A) 12p+ 25 <100

C) 12p+ 25 ≥100

D) 12p-25 ≥100

F) 12p≥ 100-25

The inequality 12p+ 25 <100 represents the condition where the customer has fewer than 100 points, so they have not yet earned the first gift certificate.

The inequality 12p+ 25 ≥100 represents the condition where the customer has 100 points or more, so they have earned the first gift certificate.

The inequality 12p-25 ≥100 represents the condition where the customer has at least 100 points, so they have earned the first gift certificate.

The inequality 12p≥ 100-25 represents the condition where the customer has at least 100 points, so they have earned the first gift certificate.