1. Max had 3/4 as many games as Corey. When Corey gave half of his games to Max, he had 30 fewer games than his friend. How many games did Corey have at first?

Question

2. Chase had 1/8 as many magnets as Gavin. Gavin gave a quarter of his magnets to Chase. Then Gavin had 5 fewer magnets than his friend. How many magnets does Gavin have now?

Answer 1

Corey has = x number of games
So Max has = 3/4x number of games.
Now, Corey gave half of his games to Max
So, Corey gave = x/2 games to Max
So, Now Max has now, (3/4x + x/2) games
= (3x + 2x)/4 = 5x/4 games.
Now, Max have (5x/4 - x) = x/4 more games than Corey
So, x/4 = 30
So x = 30 * 4 = 120 games.
So Corey have 120 games at first.

Answer 2

Let Gavin has (x) magnets
then Chase has x/8 magnets
A/q Gavin gave quarter of his magnets to Chase
So he has now = x - x/4 = 3x/4
and Chase has now = x/8 + x/4 = 3x/8
=> 3x/4 - 3x/8 = 5 => 3x/8 = 5 => x = 40/3
So Gavin has now = 3x/4 = 3x/4 * 40/3 = 10 magnets