Jake begins the summer with 1,000 marbles in his collection. He aims to have a minimum of 500 marbles left by the end of the summer. Each week, he gives away 100 marbles to friends.

Question

Which inequality should be used to determine the number of weeks (w) Jake can continue giving away marbles?

(1 point)
Responses

1000−100w≥500

1000−100w>500

1000−100w<500

1000−100w≤500
Question 2
(1 point)
Jake can give away marbles for at least? at most? less than? Greater than? Exactly?
5 weeks.

Answer 1

To determine the number of weeks (w) Jake can continue giving away marbles while ensuring he has at least 500 marbles left, we need to set up an inequality.

Starting with the initial number of marbles he has, which is 1,000, we can express how many marbles he has left after giving away 100 marbles each week for 'w' weeks:

\( 1000 - 100w \)

Jake wants to have at least 500 marbles remaining, so we set up the inequality:

\( 1000 - 100w \geq 500 \)

The correct inequality to use is:

1000−100w≥500

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For the second question, we need to determine how many weeks he can give away marbles. We can solve the inequality from the first question:

1. Start with the inequality: \( 1000 - 100w \geq 500 \)

2. Subtract 1000 from both sides: \( -100w \geq 500 - 1000 \)

3. Simplify the right side: \( -100w \geq -500 \)

4. Now, divide both sides by -100 (remember, when dividing by a negative number, we flip the inequality sign): \( w \leq 5 \)

So, Jake can give away marbles for at most 5 weeks.