A dad holds 5 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 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?

Expert Answers

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In this question, we have to determine the % error of the estimate of the son. If he estimated the amount of money held in his dad's hand within 5% error, he can have all the coins. Otherwise, he will not have any.

The son's estimate is 81 cents, while the actual amount held in his dad's hand is 90 cents. The percentage error in the estimation is calculated by using the error and the actual value.

Error in the estimate = amount estimated - actual amount

= 81 cents - 90 cents = - 9 cents

Actual value = 90 cents

% error = (error/actual value) x 100 = (-9 cents / 90 cents) x 100

= 10%

The boy has estimated 10% less amount than the actual value. Since his estimate is off by more than 5%, the son will not get any money from his dad.

Hope this helps.

 

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