A dad holds five coins in his hand. He tells his son that if he can guess the amount of money he is holding within 5% error, he can have the money. The son guesses that he is holding 81 cents. The dad opens his hand and displays 90 cents. Does the son guess close enough to receive the money from his father?

To find out if the son's guess was close enough to the actual amount, we need to calculate 5% of the actual amount (90 cents) and compare it to the difference between the guess (81 cents) and the actual amount.

Step 1: Calculate 5% of the actual amount. 5% of 90 cents = 0.05 × 90 = 4.5 cents

Step 2: Determine the permissible error range. The son's guess must be within 4.5 cents above or below the actual amount to be within the 5% error margin.

Step 3: Find the lower and upper bounds of the permissible range. 

Lower bound = Actual amount - Error margin = 90 cents - 4.5 cents = 85.5 cents

Upper bound = Actual amount + Error margin = 90 cents + 4.5 cents = 94.5 cents

Step 4: Check if the son's guess falls within this range. The son's guess of 81 cents is lower than the lower bound of 85.5 cents; thus, it is not within 5% of the actual amount.

Conclusion: The son's guess was not close enough to receive the money from his father.