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% 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?
Nope.
0.90 * 0.05 = 0.05
To determine if the son's guess was close enough to receive the money from his father, we need to calculate the allowed error range of 5% and compare it with the difference between the son's guess and the actual amount held by the father.
Step 1: Calculate the allowed error range:
5% of 90 cents = 0.05 * 90 = 4.5 cents
Step 2: Calculate the difference between the son's guess and the actual amount:
|Guess - Actual| = |81 - 90| = 9 cents
Step 3: Compare the difference with the allowed error range:
9 cents > 4.5 cents
Since the difference between the son's guess and the actual amount held by the father is greater than the allowed error range of 5%, the son did not guess close enough to receive the money from his father.
To determine if the son's guess was close enough to receive the money from his father, we need to calculate the 5% error range.
First, we calculate 5% of 90 cents:
(5/100) * 90 = 4.5 cents
Then, we find the lower and upper boundaries of the range by subtracting and adding the error value from the actual amount of money held by the father:
90 - 4.5 = 85.5 cents (lower boundary)
90 + 4.5 = 94.5 cents (upper boundary)
Since the son's guess was 81 cents, we need to see if it falls within this range.
81 cents is less than the lower boundary of 85.5 cents. Therefore, the son's guess is not within the 5% error range, and he would not receive the money from his father.