Modeling Inequalities in Real-Life Situations

Real-World Situation:

In a busy city, Jimmy runs a small food stall where he serves customers daily. Jimmy had 834 customers a day, and at one point he noticed that he had 14 more customers than usual. Meanwhile, he knows that 978 customers visited his stall on a different day, where he took away 10 from each group as a promotion. To represent this scenario mathematically, we can use the inequality:

834 + 14s > 978 - 10s

Here, 's' represents the number of additional customers Jimmy had on the day he noticed 14 more customers.

Solution:

To solve the inequality, we can start by simplifying it:

834 + 14s > 978 - 10s

14s + 10s > 978 - 834

24s > 144

s > 6

Therefore, Jimmy had more than 6 additional customers on the day he noticed the increase in the number of customers compared to his regular count of 834.

Question:

What does the inequality 834 + 14s > 978 - 10s represent in the real-world situation involving Jimmy's food stall?

Answer:

The inequality 834 + 14s > 978 - 10s represents the comparison of the number of customers Jimmy had on a regular day (834 customers) to the number of customers he had on a different day where he noticed 14 more customers, and also took away 10 customers per group.