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Amelia has a jar full of dimes (xx) and quarters (yy). She has a total of 90 coins. The coins total to $14.70. Write the equations that represent this situation.

[Use decimals to represent that dimes are 0.10 and quarters are 0.25]

1 answer

Let's denote the number of dimes as \( x \) and the number of quarters as \( y \). We can set up the following equations based on the information provided:

  1. The total number of coins (dimes and quarters) is 90: \[ x + y = 90 \]

  2. The total value of the coins is $14.70. Since dimes are worth $0.10 and quarters are worth $0.25, we can express this as: \[ 0.10x + 0.25y = 14.70 \]

So the two equations that represent the situation are:

  1. \( x + y = 90 \)
  2. \( 0.10x + 0.25y = 14.70 \)