Question

Alfie has a collection of 528 trading cards, and ellie has a collection of 609 trading cards. at the end of each month, alfie buys a box of 50 trading cards and ellie buys a box of 42 trading cards. after how many months will alfie have more trading cards than ellie?

Answer 1

Alfie starts with fewer cards but adds more each month than Ellie does. After setting up inequality equations for their collections and solving for m, it is found that Alfie will have more cards than Ellie after 11 full months.

Step-by-step explanation:

The question poses a linear growth problem where Alfie and Ellie are both adding to their trading card collections at a constant rate per month. Alfie starts with 528 cards and gains 50 each month, while Ellie begins with 609 cards and gains 42 each month. The goal is to determine after how many months Alfie will have more cards than Ellie.

Step-by-step Explanation

1. Let the number of months be represented by m.
2. Alfie's collection can be modeled by the equation: 528 + 50m.
3. Ellie's collection can be modeled by the equation: 609 + 42m.
4. We want to find out when Alfie's collection will surpass Ellie's, meaning when 528 + 50m > 609 + 42m.
5. Subtracting 42m from both sides gives us 528 + 8m > 609.
6. Subtracting 528 from both sides results in 8m > 81.
7. Dividing both sides by 8 to solve for m gives us m > 81/8.
8. Since m represents full months, Alfie will have more cards than Ellie after 11 full months because 81/8 is just over 10, and you can't have a fraction of a month.