Which inequality can be used to find w, the number of weeks after starting his collection when Lawrence will have more than 750 baseball cards in his collection?
Understand the Problem
The question is asking which inequality represents the number of weeks, w, it takes for Lawrence to have more than 750 baseball cards, considering he starts with 200 cards and adds 25 each week.
Answer
The correct inequality is $$ 25w + 200 > 750 $$
Answer for screen readers
The inequality representing when Lawrence will have more than 750 baseball cards is: $$ 25w + 200 > 750 $$
Steps to Solve
- Identify the starting amount of cards
Lawrence starts with 200 baseball cards. This is the initial value we will use in our inequality.
- Determine the weekly addition of cards
Each week, Lawrence purchases 25 additional baseball cards. This means that for each week $w$, he will accumulate $25w$ more cards.
- Combine the total amount of cards
The total number of baseball cards after $w$ weeks can be represented as: $$ 200 + 25w $$
- Set up the inequality for more than 750 cards
We need to find when the total number of cards is greater than 750, which gives us the inequality: $$ 200 + 25w > 750 $$
- Choose the correct answer option
Among the provided options, the correct inequality that represents the scenario is: $$ 25w + 200 > 750 $$
The inequality representing when Lawrence will have more than 750 baseball cards is: $$ 25w + 200 > 750 $$
More Information
This inequality indicates that after a certain number of weeks, the total number of cards Lawrence owns, including his starting cards and the cards purchased weekly, will exceed 750.
Tips
- Confusing the operations: Be careful not to switch the inequality direction; since we're looking for when the total exceeds 750, it should be a 'greater than' inequality.
- Forgetting to include the starting number of cards (200) when forming the inequality.
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