Solve each of the following problems using one or more...

Solve each of the following problems using one or more conversion factors: a. A container holds 0.500 qt of liquid. How many milliliters of lemonade will it hold? b. What is the mass, in kilograms, of a person who weighs $175 \mathrm{lb} ?$ c. An athlete has $15 \%$ body fat by mass. What is the weight of fat, in pounds, of a 74 -kg athlete? d. A plant fertilizer contains $15 \%$ nitrogen (N) by mass. In a container of soluble plant food, there are 10.0 oz of fertilizer. How many grams of nitrogen are in the container?

Solve each of the following problems using one or more conversion factors:
a. A container holds 0.500 qt of liquid. How many milliliters of lemonade will it hold?
b. What is the mass, in kilograms, of a person who weighs $175 \mathrm{lb} ?$
c. An athlete has $15 \%$ body fat by mass. What is the weight of fat, in pounds, of a 74 -kg athlete?
d. A plant fertilizer contains $15 \%$ nitrogen (N) by mass. In a container of soluble plant food, there are 10.0 oz of fertilizer. How many grams of nitrogen are in the container?

Key Concepts

Percentage Calculations

Percentage calculations determine what portion of a whole is represented by a certain component. In the context of these problems, percentages are used to find the weight of a component (such as body fat or nitrogen content) by multiplying the total mass by the percentage expressed as a decimal. This concept is widely applicable in various fields, including nutrition, chemistry, and finance.

Conversion Factors

Conversion factors are ratios used to express the equivalence between two different units. They enable the conversion of quantities from one unit system to another by multiplying the original measurement by a fraction that represents the relationship between the two units. This is essential in solving problems where the units given do not match the units required in the answer.

Dimensional Analysis

Dimensional analysis is a systematic method for converting one set of measurements to another. By using conversion factors, the unwanted units cancel out, leaving only the desired units. This technique ensures that the calculations are logically and mathematically consistent, and it spotlights any potential errors in unit handling.

Unit Conversion

Unit conversion involves changing a measurement from one unit to another, such as converting quarts to milliliters or pounds to kilograms. This process is critical when dealing with mixed measurement systems (metric and imperial) and relies on the correct use of conversion factors to maintain the accuracy of the measurement during the transformation.

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