# The amount a customer can be overcharged or undercharged due to the possible inaccuracy in the scale. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.7, Problem 112E
To determine

## The amount a customer can be overcharged or undercharged due to the possible inaccuracy in the scale.

Expert Solution

The amount a customer can be overcharged or undercharged lies in the interval [0.585,0.585]_.

### Explanation of Solution

Given:

The coffee merchant sells 3 lb of Hawaiian Kona at $6.50 per pound. The merchant’s scale is inaccurate within ±0.03lb. Calculation: The amount a customer will pay for 3 lb of Kona is obtained as follows. 3×6.50=19.5 Therefore, the amount a customer will pay for 3 lb of Kona is$19.5.

Note that, when the error is 0.03lb, 1 lb of Kona will be measured as 1+0.03=1.03lb and when the error is 0.03lb, 1 lb of Kona will be measured as 10.03=0.97lb

Now, obtain the amount a customer will pay for 3 lb of Kona when the measuring error is 0.03lb.

3(1+0.03)×6.50=3(1.03)×6.50=3.09×6.50=$20.085 Similarly, obtain the amount a customer will pay for 3 lb of Kona when the measuring error is 0.03lb. 3(10.03)×6.50=3(0.97)×6.50=2.91×6.50=$18.915

Then, the cost of three pounds of coffee with error lies in the interval [18.915,20.085].

Now, the amount a customer will pay for 3 lb of Kona when the measuring error is 0.03lb, is obtained as follows.

19.520.085=0.585

And the amount a customer will pay for 3 lb of Kona when the measuring error is 0.03lb, is obtained as follows.

19.518.915=0.585

Thus, amount a customer can be overcharged or undercharged lies in the interval [0.585,0.585]_.

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