(a) How many liters of wine can be held in a wine barrel...

(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

Key Concepts

Unit Conversion

Unit conversion involves translating a measurement expressed in one unit to its equivalent in another, using a standardized conversion factor. In problems like converting gallons to liters, the conversion factor (approximately 1 gallon = 3.785 liters) is used to determine the equivalent volume in the new unit.

Ratios and Proportions

Ratios and proportions are mathematical tools used to compare relative quantities and solve problems where two quantities maintain a consistent relationship. They are essential in setting up equations that relate the original unit to the desired unit, as well as in adjusting dosages based on weight.

Dosage Calculation

Dosage calculation refers to determining the precise amount of medication to be administered, usually by multiplying the recommended amount per unit of measure (e.g., mg per kg) by the patient's weight. This ensures that the dosage is both effective and safe for the individual's body mass.

Transcript

00:01 So here we want to go ahead and convert 31 gallons into liters.

00:05 And in order to do this, we're going to have to do a little bit of dimensional analysis.

00:10 And we have to use a lot of conversion factors.

00:13 And the key to this problem is we want to, again, we have to get to gallons, from gallons to liters.

00:19 And from gallons, we can go to cubic inches.

00:23 And then from cubic inches, we can get to cubic centimeters.

00:27 And then from cubic centimeters, we can go into liters.

00:30 So that's pretty much how it's going to play out in this problem.

00:33 So if you want to go ahead and start, i'll go ahead and have my little drawing here.

00:38 We'll start with 31 gal.

00:40 I'll just put gal for short.

00:43 So we start with 31 gallons.

00:46 And again, we mentioned that we want to go ahead and convert from gallons, and we want to go into cubic inches.

00:54 And so we know in terms of this conversion factor that is useful to know, for every one gallon, so we'll pull gal again for short, there is 231 cubic inches.

01:12 Let me actually make that a little bit easier to read cubic inches like so.

01:19 So again, right now we've done 31 gallons, and then for every one gallon, we have this many cubic inches.

01:25 And now we'll have to convert our cubic inches into cubic centimeters.

01:28 And so another conversion factor is for every cubic inch, we're going to have a certain amount of cubic centimeters.

01:36 So if we want to go ahead and write it like so, remember, every cubic inch here, and we have to write cubic inch like this, we can write that for every cubic inch, there is 2 .54 cubed cubic centimeters.

02:02 And if you want, you don't have to necessarily draw it out this way...

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