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 create an inequality for the amount of money Carlos needs to earn each Saturday morning, we first note the following:

1. Carlos needs to save at least $200 over four weeks.
2. His mom gives him $30, so he will start with that amount.
3. Let \( x \) represent the amount of money Carlos earns each Saturday morning.
4. He will earn money for four weeks.

Over the four weeks, he will earn \( 4x \) (since he earns \( x \) each Saturday for four Saturdays).

Now we can set up the inequality to represent the total amount of money Carlos will have after four weeks, which includes the $30 given by his mom:

\[ 30 + 4x \geq 200 \]

To solve this inequality for \( x \), we can subtract 30 from both sides:

\[ 4x \geq 200 - 30 \]

\[ 4x \geq 170 \]

Next, divide both sides by 4:

\[ x \geq \frac{170}{4} \]

\[ x \geq 42.5 \]

So the inequality we set up is:

\[ x + 30 \geq 200 \]

And Carlos must earn at least $42.50 each Saturday morning to have at least $200 in four weeks.

Final answer: \[ x + 30 \geq 200, \text{ where } x \text{ is the amount Carlos earns each Saturday morning. Carlos must earn at least } $42.50 \text{ each Saturday morning.} \]