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

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?

thucuc · Answer

Solution:    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.

thucuc · Answer

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

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