Question

There is a total of 27 quarters stacked in four piles. The first pile has 5 fewer than the second pile. The second pile has 4 more than the third pile. The fourth pile has three times as many as the second pile. How many quarters are in the fourth pile?

Answer 1

Answer: 18 quarters

Step-by-step explanation:

second pile = x

first pile = x - 5

third pile = x - 4

fourth pile = 3x

total amount of quaters = 27

x + x - 5 + x - 4 + 3x = 27

6x = 36 x = 6

fourth pile = 3(6) = 18

Answer 2

Note that:

• 27 quarters = 4 piles = 1st pile + 2nd pile + 3rd pile + 4th pile
• 1st pile = 2nd pile - 5 = 3rd pile - 1
• 2nd pile = 1st pile + 5 = 3rd pile + 4
• 3rd pile = 1st pile - 1 = 2nd pile - 4
• 4th pile = 3(2nd pile)

This means that...

• 27 quarters = (2nd pile - 5) + (2nd pile) + (2nd pile - 4) + 3(2nd pile)

First, let's find the number of quarters in 2nd pile.

Open the brackets.

• 27 quarters = (2nd pile - 5) + (2nd pile) + (2nd pile - 4) + 3(2nd pile)
• => 27 quarters = 2nd pile - 5 + 2nd pile + 2nd pile - 4 + 3(2nd pile)

Combine like terms.

• => 27 quarters = (-5 - 4) + 6(2nd pile)

Simplify the RHS.

• 27 quarters = -9 + 6(2nd pile)

Add 9 both sides.

• 27 + 9 = 6(2nd pile)
• => 36 quarters = 6(2nd pile)

Divide 6 both sides.

• => 6 quarters = 2nd pile

Now, substitute the number of quarters in 2nd pile in it's equation.

• 4th pile = 3(2nd pile)
• => 4th pile = 3(6)
• => 4th pile = 18 quarters.