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 solve this problem, we need to determine how much Carlos still needs to earn after receiving the initial $30 given by his mom.

1. Total Savings Goal: Carlos wants to save at least $200.
2. Amount Given by Mom: He receives $30.
3. Remaining Amount to Earn: Therefore, the amount Carlos still needs to earn is:

\[ 200 - 30 = 170 \]

4. Earnings Over Four Weeks: Carlos has four Saturdays to earn this remaining amount, and we will denote the amount he earns each Saturday morning as \( x \).

5. Total Earnings Calculation: Over four Saturdays, Carlos will earn \( 4x \) because he earns \( x \) each Saturday.

6. Inequality Setup: In order for Carlos to reach his savings goal:

\[ 30 + 4x \geq 200 \]

7. Subtract $30 from both sides:

\[ 4x \geq 200 - 30 \]

\[ 4x \geq 170 \]

8. Divide both sides by 4:

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

\[ x \geq 42.5 \]

Conclusion:

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

Solution Description:

The solutions to the inequality \( x \geq 42.5 \) imply that any amount Carlos earns per Saturday that is $42.50 or greater will result in him having at least $200 saved at the end of the four weeks. If he earns less than $42.50 in any week, he will fall short of his savings goal.

Answer 2

wrong