Carlos is hoping to save at least $200 in the next four weeks. His mom gives him $30, and he earns money each Saturday morning at his grandmother’s store. Write an inequality for the amount of money Carlos will need to earn each Saturday morning, and describe the solutions. Assume Carlos will earn the same amount each Saturday morning.(2 points)

Question

__x+__≥__, where x is the amount Carlos earns each Saturday morning. Carlos must earn at least $__ each Saturday morning to have at least $200 in four weeks.

Answer 1

To write the inequality for the amount of money Carlos needs to earn each Saturday morning, let's define:

• \( x \): the amount of money Carlos earns each Saturday morning.

Carlos has $30 from his mom, and he wants to save at least $200 in total over the next four weeks. He will be working for 4 Saturdays, which means he will earn \( 4x \) over the four weeks.

The total amount Carlos will have after four weeks, including the initial $30, can be expressed as:

\[ 30 + 4x \]

Since he wants to save at least $200, we can set up the inequality:

\[ 30 + 4x \geq 200 \]

Now, we can isolate \( x \) in the inequality:

1. Subtract 30 from both sides: \[ 4x \geq 200 - 30 \] \[ 4x \geq 170 \]

2. Divide both sides by 4: \[ x \geq \frac{170}{4} \] \[ x \geq 42.5 \]

Thus, the completed inequality can be written as:

\[ x \geq 42.5 \]

This means Carlos must earn at least $42.50 each Saturday morning to achieve his goal of saving at least $200 in the next four weeks. The solutions to this inequality represent all the amounts \( x \) that are $42.50 or greater.