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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 ( at least, at most less than greater than equal to)
5 weeks.
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Answer 1

Let's analyze the questions one by one.

Question 1

Jake begins 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. We can set up the inequality to represent this situation:

1. Start with 1,000 marbles.
2. Subtract 100 marbles for each week (w) he gives away marbles.
3. He wants to have at least 500 marbles left.

The inequality that represents this situation is:

\[ 1000 - 100w \geq 500 \]

So, the correct response is: 1000−100w≥500 (1000 minus 100 w is greater than or equal to 500)

Question 2

We need to solve the inequality to find out how many weeks (w) Jake can give away marbles.

Starting with the inequality: \[ 1000 - 100w \geq 500 \]

Subtract 1000 from both sides: \[ -100w \geq 500 - 1000 \] \[ -100w \geq -500 \]

Now, divide by -100. Remember that when dividing by a negative number, the inequality sign flips: \[ w \leq 5 \]

This means Jake can give away marbles for at most 5 weeks.

So, the final answer for Question 2 is: at most 5 weeks.