To solve this problem, we need to determine how much Carlos still needs to earn after receiving the initial $30 given by his mom.
- Total Savings Goal: Carlos wants to save at least $200.
- Amount Given by Mom: He receives $30.
- Remaining Amount to Earn: Therefore, the amount Carlos still needs to earn is:
\[ 200 - 30 = 170 \]
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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 \( x \).
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Total Earnings Calculation: Over four Saturdays, Carlos will earn \( 4x \) because he earns \( x \) each Saturday.
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Inequality Setup: In order for Carlos to reach his savings goal:
\[ 30 + 4x \geq 200 \]
- Subtract $30 from both sides:
\[ 4x \geq 200 - 30 \]
\[ 4x \geq 170 \]
- 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.