For one photography session, Dexter earns no less than $50, but no more than $100. Which inequality can be used to represent his earnings, e?
A. [tex]$e \geq 50$[/tex] or [tex]$e \leq 100$[/tex]
B. [tex]$e\ \textgreater \ 50$[/tex] or [tex]$e\ \textless \ 100$[/tex]
C. [tex]$50\ \textless \ e\ \textless \ 100$[/tex]
D. [tex]$50 \leq e \leq 100$[/tex]
Answer (1)
Dexter's earnings are no less than 50 , w hi c h t r an s l a t es t o e \geq 50$.
His earnings are no more than 100 , w hi c h t r an s l a t es t o e \leq 100$.
Combining these inequalities, we represent his earnings as 50 ≤ e ≤ 100 .
The inequality representing Dexter's earnings is 50 ≤ e ≤ 100 .
Explanation
Understanding the Problem Let's analyze the problem. Dexter's earnings, represented by 'e', have a minimum and maximum value. The problem states that he earns 'no less than' $50, meaning his earnings are at least $50, and 'no more than' $100, meaning his earnings are at most $100. We need to combine these two conditions into a single inequality.
Expressing the Minimum Earnings The phrase 'no less than 5 0 ′ t r an s l a t es t o e \geq 50$. This means Dexter's earnings are greater than or equal to $50.
Expressing the Maximum Earnings The phrase 'no more than 10 0 ′ t r an s l a t es t o e \leq 100$. This means Dexter's earnings are less than or equal to $100.
Combining the Inequalities Combining these two inequalities, we get 50 ≤ e ≤ 100 . This inequality states that Dexter's earnings are between $50 and $100, inclusive.
Final Answer Therefore, the inequality that represents Dexter's earnings is 50 ≤ e ≤ 100 .
Examples
Imagine you're saving money for a new video game. You know you need at least $50 to buy it, but you don't want to spend more than $100. This situation can be represented by the inequality 50 ≤ e ≤ 100 , where 'e' is the amount you spend on the game. This type of problem helps you understand how to define boundaries and constraints in real-life scenarios, such as budgeting, setting goals, or defining acceptable ranges for measurements.
