A coffee merchant sells a customer 3 lb of Hawaiian Kona at $9.75 per pound. The merchant's scale is accurate to within ±0.03 lb. By how much could the customer have been overcharged or undercharged because of possible inaccuracy in the scale? (Round your answer to the nearest whole cent.)
To find out how much the customer could have been overcharged or undercharged due to the scale's inaccuracy, we need to calculate the maximum and minimum possible weight of the coffee purchased.
The actual weight of the coffee purchased is 3 lb, which we'll refer to as the "target weight."
The scale's accuracy is given as ±0.03 lb, which means the actual weight could be slightly higher or slightly lower than the target weight.
To find the maximum possible weight, we add the scale's upper limit of 0.03 lb to the target weight: 3 lb + 0.03 lb = 3.03 lb.
To find the minimum possible weight, we subtract the scale's lower limit of 0.03 lb from the target weight: 3 lb - 0.03 lb = 2.97 lb.
Now that we have the maximum and minimum possible weights, we can calculate the maximum and minimum amounts charged.
The price per pound is $9.75, so the maximum amount charged would be the price per pound multiplied by the maximum possible weight: $9.75 * 3.03 lb = $29.53.
The minimum amount charged would be the price per pound multiplied by the minimum possible weight: $9.75 * 2.97 lb = $28.87.
Therefore, the customer could have been overcharged by $0.66 ($29.53 - $28.87) or undercharged by $0.66 ($28.87 - $29.53) due to the scale's inaccuracy.
Rounding to the nearest whole cent, the customer could have been overcharged or undercharged by $0.66.