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, we first need to consider how much total money he needs to save, which is at least $200. He already has $30 from his mom.

Let \( x \) represent the amount of money Carlos earns each Saturday morning. Since he earns money for 4 Saturdays, the total amount he will earn in 4 weeks is \( 4x \).

Now we can set up the inequality as follows:

\[ 30 + 4x \geq 200 \]

To isolate \( x \), we can subtract 30 from both sides:

\[ 4x \geq 200 - 30 \] \[ 4x \geq 170 \]

Next, we divide both sides by 4:

\[ x \geq \frac{170}{4} \] \[ x \geq 42.5 \]

So, the complete inequality will be:

\[ 4x + 30 \geq 200, \text{ where } x \text{ is the amount Carlos earns each Saturday morning.} \]

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

In summary, the answer is: \[ 4x + 30 \geq 200, \text{ where } x \text{ is the amount Carlos earns each Saturday morning. Carlos must earn at least } $42.50 \text{ each Saturday morning.} \]