1. 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% percentage error he can have the money. The son guesses that he is holding 81 cents. The dad opens his hand and displays 90 cents. Did the son guess close enough to receive the money from his father?
.81 + .05(.81) = ?
.8505
yes
yes
To determine if the son's guess was close enough to receive the money from his father, we need to calculate the allowable error within the given range of 5% percentage error.
First, we calculate the upper and lower limits of the allowable range:
Upper limit = (100 + 5)% × 81 cents = 1.05 × 81 cents = 85.05 cents
Lower limit = (100 - 5)% × 81 cents = 0.95 × 81 cents = 76.95 cents
Since the father is holding 90 cents, we can compare it with the lower and upper limits of the allowable range:
76.95 cents ≤ 90 cents ≤ 85.05 cents
As 90 cents falls within the range of 76.95 cents to 85.05 cents, the son's guess is close enough to receive the money from his father.