Question

Daniel's father gave him 130 baseball cards. Each week, Daniel purchases 25 more cards to add to his collection. Which inequality can be used to find "w," the number of weeks after starting his collection when Daniel will have more than 500 baseball cards in his collection?

A) 25w + 130 > 500
B) 130w + 25 > 500
C) 130w + 25 < 500
D) 25w + 130 < 500

Answer 1

The inequality to find out when Daniel will have more than 500 baseball cards, starting with 130 and adding 25 each week, is 25w + 130 > 500. This is because 'w' represents the number of weeks, and the inequality reflects the total cards exceeding 500.

Step-by-step explanation:

The student is tasked with determining the inequality that represents the situation where Daniel will have more than 500 baseball cards after receiving 130 cards and buying 25 more each week. The correct inequality to model this situation is: 25w + 130 > 500. This is because Daniel starts with 130 cards and for each week, denoted as 'w', he adds 25 more cards. To find out after how many weeks he will have more than 500 cards, we need to add 25 times the number of weeks to the initial amount of cards and set this sum to be greater than 500.

The step-by-step explanation is as follows:

1. 
   
3. Start with the initial number of cards: 130.
4. 
   
6. Add 25 cards for each week: 25w.
7. 
   
9. Combine both to form an expression: 25w + 130.
10. 
    
12. Set this expression greater than 500 to determine when he will have over 500 cards.