Jamal has a drawer containing green socks, purple socks, and orange socks. After adding more purple socks, Jamal noticed that there is now a chance that a sock randomly selected from the drawer is purple. How many purple socks did Jamal add?
Pick one
Solutions — 2
Solution 1
After Jamal adds purple socks, he has purple socks and total socks. This means the probability of drawing a purple sock is , so we obtain Since , the answer is .
Solution 2
1. Jamal initially has 6 green socks, 18 purple socks, and 12 orange socks. Therefore, the total number of socks initially is:
2. Let be the number of purple socks Jamal added. After adding purple socks, the total number of socks becomes:
3. The number of purple socks after adding purple socks is:
4. According to the problem, the probability that a randomly selected sock is purple is now 60%. Therefore, we can set up the following equation:
5. Converting 60% to a fraction, we get:
6. Cross-multiplying to solve for :
7. Expanding both sides:
8. Subtracting from both sides:
9. Subtracting 90 from both sides:
10. Dividing both sides by 2:
Therefore, Jamal added purple socks.