To determine the number of weeks (w) Jake can continue giving away marbles while ensuring he has at least 500 marbles left, we can set up the inequality based on the information provided.
He starts with 1,000 marbles and gives away 100 marbles each week. After \( w \) weeks, the number of marbles he will have left can be expressed as:
\[ 1000 - 100w \]
We want this amount to be at least 500 marbles, so we set up the inequality:
\[ 1000 - 100w \geq 500 \]
This means that the correct inequality to determine the number of weeks is:
1000−100w≥500
In response to Question 2, let's solve the inequality to find the number of weeks:
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Start with the inequality: \[ 1000 - 100w \geq 500 \]
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Subtract 1000 from both sides: \[ -100w \geq 500 - 1000 \] \[ -100w \geq -500 \]
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Divide by -100 (remember to reverse the inequality when dividing by a negative): \[ w \leq 5 \]
Thus, Jake can give away marbles for a maximum of 5 weeks.