Question

Lynn bought 7 new football trading cards to add to her collection. The next day when she moved them to another location, half of her football trading card collection got ruined from water damage. There are now only 45 cards left. How many football cards did Lynn start with?

a) 90
b) 104
c) 98
d) 114

Answer 1

Lynn originally had 90 football trading cards before water damage ruined half of her collection, leaving her with 45 cards. By doubling the number of remaining cards, we can determine that she initially had 90 cards in total (option a).

Step-by-step explanation:

The student is asking how many football trading cards Lynn originally had, given that half of her collection was ruined by water damage, leaving her with 45 intact cards.

To solve this, we must find the total before the water damage occurred. Since the 45 cards represent the half of her collection that was not damaged, we multiply 45 by 2 to find the original number of cards.

Therefore, Lynn started with 90 football trading cards.

We can set up the equation:

`45 = \( (1)/(2) \) * (original collection + 7 new cards).`

Let's call the original collection 'x'. So, we have

`45 = \( (1)/(2) \) * (x + 7).`

To solve for x, we first multiply both sides of the equation by 2, getting 90 = x + 7.

Subtracting 7 from both sides of the equation, we find that x = 83.

Adding the 7 new cards to x, we confirm that Lynn's total collection before the water damage was 90 cards, which means the correct answer is option (a).