Question

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.

Answer 1

To determine the inequality that represents the situation where Jake starts with 1,000 marbles and gives away 100 marbles each week while wanting to have at least 500 marbles left, we can set up the inequality as follows:

1. Start with the total number of marbles Jake has: 1,000.
2. Subtract the number of marbles he gives away each week, which is 100 times the number of weeks (\(w\)).
3. Set this expression to be greater than or equal to the minimum amount of marbles he wants left, which is 500.

The inequality would be:

\[ 1000 - 100w \geq 500 \]

Therefore, the correct choice is:

**1000−100w≥500**

---

For the second question, to find out how many weeks Jake can give away marbles:

Starting with the inequality \( 1000 - 100w \geq 500 \):

1. Solve for \(w\):
\[
1000 - 100w \geq 500
\]
\[
1000 - 500 \geq 100w
\]
\[
500 \geq 100w
\]
\[
5 \geq w
\]

This means Jake can give away marbles for a maximum of **5 weeks**.