Q67E - Chemistry (OpenStax)

Question

Is a 197-lb weight lifter light enough to compete in a class limited to those weighing 90 kg or less?

Step-by-Step Solution

Answer

Yes, the weight lifter is enough to compete.

Step 1: Describing the pound and kilogram terms

A pound is a unit of mass in the British imperial and US customary unit system used to measure the mass. It is denoted by the lb.

\(1\,\,{\rm{lb}}\,\, = \,\,0.453592\,\,{\rm{kg}}\)

A kilogram is used to measure mass in the international system of units. It is denoted by kg. This unit is used to measure the quantity in the SI unit system. It is considered to be the most standard unit of mass.

\(1\,\,{\rm{kg}}\,\, = \,2.20462\,{\rm{lb}}\)

Step 2: Converting the units from pound into kilogram using the conversion factor

The given mass of the weight lifter is 197 lb.

While we know 

\(1\,\,{\rm{lb}}\,\, = \,\,0.453592\,\,{\rm{kg}}\)

Thus,

\(\begin{aligned}{\underline{\phantom{xx}}}197\,\,{\rm{lb}}\,\,\\ = \,\,197\,\left( {{\rm{lb}}\, \times \,\frac{{0.453592\,\,{\rm{kg}}}}{{{\rm{lb}}}}} \right)\,\,\\ = \,\,197\,\, \times \,\,0.453592\,{\rm{kg}}\,\,\\ = \,\,89.357624\,\,{\rm{kg}}\\\, \approx 90\,\,{\rm{kg}}\end{aligned}\)

The mass of the weight lifter is 89.357624 kg, equivalent to 89.4 kg. Therefore, the weight lifter can compete in a class limited to weighing 90 kg or less.