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If Mike had a total of $4.35 in nickels and there were five more nickels than he thought, how many nickels did he originally believe he had?

  1. 78

  2. 82

  3. 86

  4. 87

The correct answer is: 82

To determine how many nickels Mike originally believed he had, we start by recognizing that the total amount of money he has, $4.35, is equivalent to 435 cents. Since nickels are worth 5 cents each, we can express the number of nickels he has in terms of cents. Let's denote the number of nickels Mike originally believed he had as \( x \). According to the problem, Mike actually has five more nickels than he believed, which would make it \( x + 5 \) nickels. The total value of the nickels can thus be represented as: \[ 5(x + 5) = 435 \] Now we simplify and solve that equation: 1. Distributing the 5: \[ 5x + 25 = 435 \] 2. Subtracting 25 from both sides: \[ 5x = 410 \] 3. Dividing both sides by 5: \[ x = 82 \] This calculation shows that Mike originally believed he had 82 nickels. The value of the total number of nickels he actually possesses (which is 82 + 5 = 87 nickels) indeed totals to