Carlos works as a busboy making per hour and as a theater usher making per hour. Let be the number of hours he works as a busboy this month, and let be the number of hours he works as an usher. His goal this month is to earn at least total. Using the values and variables given, write an inequality describing this.

Question

Carlos works as a busboy making per hour and as a theater usher making per hour. Let be the number of hours he works as a busboy this month, and let be the number of hours he works as an usher. His goal this month is to earn at least total. Using the values and variables given, write an inequality describing this.

Answer 1

Let's assume the number of hours Carlos works as a busboy is represented by the variable $ b $ and the number of hours he works as a theater usher is represented by the variable $ u $.

Carlos earns $ 12b $ dollars as a busboy and $ 10u $ dollars as a theater usher.

According to the problem, Carlos's goal is to earn at least $ \$120 $.

So, we can write the inequality as:
\[ 12b + 10u \geq 120 \]

This inequality states that the total earnings from working as a busboy and as a theater usher should be greater than or equal to $ \$120 $.

Answer 2

Let's write an inequality to represent Carlos's goal of earning at least a total amount this month:

Carlos's earnings as a busboy in a month = hourly rate as a busboy * number of hours worked as a busboy
Carlos's earnings as a theater usher in a month = hourly rate as a theater usher * number of hours worked as a theater usher

Total earnings = Carlos's earnings as a busboy + Carlos's earnings as a theater usher

Total earnings >= desired amount

Therefore, the inequality is:

(hourly rate as a busboy * number of hours worked as a busboy) + (hourly rate as a theater usher * number of hours worked as a theater usher) >= desired amount

Answer 3

To write an inequality describing Carlos' goal, we can use the information given in the question. Let's break it down step by step:

1. Carlos works as a busboy making $X per hour.
2. Carlos also works as a theater usher making $Y per hour.

Let's assume Carlos works for "a" hours as a busboy and "b" hours as a theater usher in a month.

So, Carlos earns "X * a" dollars from being a busboy and "Y * b" dollars from being a theater usher.

According to the question, Carlos' goal is to earn at least "C" dollars in total.

Therefore, we can write the inequality as:

X * a + Y * b ≥ C

where X, Y, a, b, and C are the given variables and total represents the minimum amount Carlos wants to earn.

Let's assume the number of hours Carlos works as a busboy is represented by the variable \( b \) and the number of hours he works as a theater usher is represented by the variable \( u \).

Let's write an inequality to represent Carlos's goal of earning at least a total amount this month:

To write an inequality describing Carlos' goal, we can use the information given in the question. Let's break it down step by step: