### Instruction: There is a total of 20 quarters stacked in four piles. The first pile has 3 fewer than the second pile. The second pile has 2 more than the third pile. The fourth pile has twice as many as the second pile. How many quarters are in the fourth pile?### Response: To find how many quarters are in the fourth pile, I need to know how many quarters are in the second pile.
To do that, I can use the information given about the relationships between the piles.
I can write an equation for each relationship using x as the number of quarters in the second pile.
The first pile has 3 fewer than the second pile, so the first pile has x - 3 quarters.
The second pile has 2 more than the third pile, so the third pile has x - 2 quarters.
The fourth pile has twice as many as the second pile, so the fourth pile has 2x quarters.
The total number of quarters is 20, so I can add up the expressions for each pile and set them equal to 20.
This gives me the equation x - 3 + x + x - 2 + 2x = 20.
To solve for x, I can combine like terms and simplify the equation.
I get 5x - 5 = 20.
Adding 5 to both sides, I get 5x = 25.
Dividing both sides by 5, I get x = 5.
This means that the second pile has 5 quarters.
To find the number of quarters in the fourth pile, I can multiply x by 2.