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. Write an inequality to determine the number of weeks Jake can continue giving away marbles and find the solution
A. 1000-100w ≥ 500; w ≥ 5
B. 1000-100w ≥ 500; w ≤ 5
C. 1000-100w ≤ 500; w ≥ 6
D. 1000+100w ≥500; w ≥ 6
The correct inequality is A. 1000-100w ≥ 500; w ≥ 5.
To solve this inequality, we can subtract 500 from both sides: 1000 - 100w - 500 ≥ 0, which simplifies to 500 - 100w ≥ 0.
We can then divide both sides by -100, but this reverses the inequality sign: w ≤ 5.
So the solution is w ≥ 5.