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Chapter 1: Problem 59

(a) How many liters of wine can be held in a wine barrel whose capacity is 31 gal? (b) The recommended adult dose of Elixophyllin", a drug used to treat asthma, is \(6 \mathrm{mg} / \mathrm{kg}\) of

Short Answer

Expert verified
The wine barrel can hold approximately 117 liters of wine, and a 50-kg person should be prescribed 300 mg of Elixophyllin.

Step by step solution

01

Conversion of gallons to liters

First, we need to convert the capacity of the wine barrel from gallons to liters. To do this, we need to know the conversion factor between gallons and liters: 1 gallon is equal to 3.78541 liters.
02

Calculate the capacity in liters

Now that we have the conversion factor, we can calculate the capacity of the wine barrel in liters: \[Capacity_{Liters} = Capacity_{Gallons} \times ConversionFactor\] \[Capacity_{Liters} = 31 \times 3.78541\]
03

Calculate the total capacity in liters

Multiply the number of gallons by the conversion factor to obtain the total capacity in liters: \[Capacity_{Liters} = 117.24771\]
04

Round the result

Round the capacity to the nearest whole number: \[Capacity_{Liters} \approx 117\] So, the wine barrel can hold approximately 117 liters of wine.
05

Calculate the Elixophyllin dose

For part (b) of the problem, we know that the recommended adult dose of Elixophyllin is \(6\, \frac{mg}{kg}\) of body weight. We need to calculate the prescribed dosage for a person weighing 50 kg: \[Dosage_{mg} = Dose_{\frac{mg}{kg}} \times Weight_{kg}\]
06

Find the prescribed dosage

Multiply the given dose by the person's weight in kg: \[Dosage_{mg} = 6 \times 50\]
07

Calculate the total dosage

Perform the calculation to find the total dosage in milligrams: \[Dosage_{mg} = 300\] So, a 50-kg person should be prescribed 300 mg of Elixophyllin.

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