Question

Select the situation that could be modeled by:

8 + 4x > 12 + 3x.
a) The cost of a meal at a restaurant with an 8-dollar base price and 4 dollars per dish.
b) The number of people attending a party with 8 initial guests and 4 more arriving every hour.
c) The temperature in a room starting at 8°C and increasing by 4°C every hour.
d) The time it takes to complete a task when starting at 8 minutes and decreasing by 3 minutes every step.

Answer 1

The situation that could be modeled by the equation 8 + 4x > 12 + 3x is option b) The number of people attending a party with 8 initial guests and 4 more arriving every hour.

Step-by-step explanation:

To understand why option b) is the correct choice, let's break down the equation. The equation represents a situation where there is a base value of 8 and an additional value of 4x, which increases as x (in this case, the number of hours) increases. On the other side of the equation, there is a base value of 12 and an additional value of 3x, which also increases as x increases.

This can be interpreted as a scenario where there are 8 initial guests at a party and 4 more guests arriving every hour. The number of guests (represented by x) increases over time, and the inequality indicates that the number of guests on one side of the equation will always be greater than the other side, as long as x is positive.

Hence, b is the correct option.