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 minus 100 w is greater than or equal to 500

1000−100w>500
1000 minus 100 w is greater than 500

1000−100w<500
1000−100w<500

1000−100w≤500

GPT-4o mini · Answer

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

Jake starts with 1,000 marbles and gives away 100 marbles for each week (w). By the end of the summer, he wants to have at least 500 marbles remaining.

The inequality can be expressed as:

\[ 1000 - 100w \geq 500 \]

This represents that the number of marbles Jake has left (1,000 marbles minus 100 marbles for each week) should be greater than or equal to 500 marbles.

Thus, the correct response is:

1000−100w≥500
(1000 minus 100 w is greater than or equal to 500)