Question 898109: A pile of coins consists of nickels, dimes, and quarters. There are 5 fewer dimes than nickels and 2 more quarters than dimes. If x equals the number of nickels, write an algebraic expression that represents the value of the pile in cents. Simplify the expression. [Hint: If x represents the number of nickels, then what do x – 5 and (x – 5) + 2 represent?]
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630)   (Show Source):
Answer by MathTherapy(10556)  (Show Source):
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A pile of coins consists of nickels, dimes, and quarters. There are 5 fewer dimes than nickels and 2 more quarters than dimes. If x equals the number of nickels, write an algebraic expression that represents the value of the pile in cents. Simplify the expression. [Hint: If x represents the number of nickels, then what do x – 5 and (x – 5) + 2 represent?]
As requested, let number of nickels be x
Then number of dimes = x - 5
Number of quarters: x - 5 + 2, or x - 3
Value of x nickels, in cents: 5x
Value of x - 5 dimes, in cents: 10(x - 5), or 10x - 50
Value of x - 3 quarters, in cents: 25(x - 3), or 25x - 75
Value of coins, in cents: 5x + 10x - 50 + 25x - 75, or 5x + 10x + 25x - 50 - 75, or 40x - 125
As seen, x - 5 represents the number of dimes, and x - 5 + 2, or x - 3 represents the number of quarters.
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