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Question

10 of 1010 of 10 Items

Question 1
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.

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
1000 minus 100 w is less than or equal to 500
Question 2
(1 point)
Jake can give away marbles for
5 weeks.
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Answer 1

To determine how many weeks (w) Jake can continue giving away marbles, we need to set up the inequality based on the information given:

Jake starts with 1,000 marbles and gives away 100 marbles each week. He wants to have at least 500 marbles left at the end of the summer.

The inequality can be formulated as:

1,000 − 100w ≥ 500

This means that after giving away 100 marbles for w weeks, he should still have at least 500 marbles remaining.

So the correct response for the inequality is: 1000−100w≥500

As for how many weeks he can continue giving away marbles, we can solve the inequality:

1. Subtract 500 from both sides: \[ 1000 - 100w - 500 ≥ 0 \] Simplifying gives: \[ 500 - 100w ≥ 0 \]

2. Rearranging gives: \[ 100w ≤ 500 \]

3. Dividing by 100 gives: \[ w ≤ 5 \]

Therefore, Jake can give away marbles for 5 weeks.

Answer 2

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