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

blank x+ blank ≥ blank
, 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

Let's define \( x \) as the amount of money Carlos earns each Saturday morning.

Carlos will earn money for four Saturdays, so the total amount he will earn from his earnings over four weeks is \( 4x \).

He also receives an initial amount of $30 from his mom. Therefore, the total amount Carlos will have after four weeks will be:

\[ 30 + 4x \]

To ensure that Carlos has at least $200 by the end of the four weeks, we can set up the following inequality:

\[ 30 + 4x \geq 200 \]

Next, we can solve this inequality for \( x \):

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

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

So, the inequality we derived is:

\[ x + 30 \geq 200 \]

With this setup, Carlos must earn at least $42.5 each Saturday morning to have at least $200 in total after four weeks.

The final statement would be: Carlos must earn at least $42.5 each Saturday morning to have at least $200 in four weeks.