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?
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?
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.
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
1. Let's break down the information given in the first question:
- Initially, Max had 3/4 as many games as Corey. Let's represent the number of games Corey had as C. Therefore, Max had (3/4)C games.
- When Corey gave half of his games to Max, Corey had C/2 games left, and Max received C/2 games.
- After this exchange, Corey had 30 fewer games than Max. So we can set up the equation: C/2 = (3/4)C - 30.
To find the value of C, we can solve this equation. Here's how:
1. Multiply both sides of the equation by 2 to eliminate the fraction: 2 * (C/2) = 2 * ((3/4)C - 30).
This simplifies to: C = (3/2)C - 60.
2. Subtract (3/2)C from both sides to remove (3/2)C from the right side of the equation: C - (3/2)C = -60.
This simplifies to: (1/2)C = -60.
3. Multiply both sides of the equation by 2 to eliminate the fraction: 2 * ((1/2)C) = 2 * (-60).
This simplifies to: C = -120.
Therefore, Corey had -120 games at first. However, since we can't have a negative number of games, we assume there was an error in the question or the given information.
2. Let's break down the information given in the second question:
- Initially, Chase had 1/8 as many magnets as Gavin. Let's represent the number of magnets Gavin had as G. Therefore, Chase had (1/8)G magnets.
- Gavin gave a quarter of his magnets to Chase. After the exchange, Gavin had (3/4)G magnets left, and Chase received (1/8)G + (1/4)G = (3/8)G magnets.
- After this exchange, Gavin had 5 fewer magnets than Chase. So we can set up the equation: (3/4)G = (3/8)G - 5.
To find the value of G, we can solve this equation. Here's how:
1. Multiply both sides of the equation by 8 to eliminate the fraction: 8 * ((3/4)G) = 8 * ((3/8)G - 5).
This simplifies to: 6G = 3G - 40.
2. Subtract 3G from both sides to remove 3G from the right side of the equation: 6G - 3G = -40.
This simplifies to: 3G = -40.
3. Divide both sides of the equation by 3 to solve for G: (3G)/3 = (-40)/3.
This simplifies to: G = -40/3.
Therefore, Gavin has -40/3 magnets at the moment. However, since we can't have a fraction of a magnet, we assume there was an error in the question or the given information.