Question

Human blood contains three primary cell types: red blood cells (RBC), white blood cells (WBC), and platelets. In an adult male, a single microliter $(1\times {10}^{-3}ml)$ of blood contains approximately $5.4\times {10}^{6}RBC,7.5\times {10}^{3}WBC$, and $3.5\times {10}^5$ platelets on average. Calculate the approximate composition of RBC in an adult human's total blood count.

• A. $1.30$%
• B. $6.21$%
• C. $60.79$%
• D. $93.79$%

Answer 1

The correct option is D $93.79$%

Start by setting up a ratio that compares RBC count to total blood cell count. Manipulate the quantities to make all the exponents the same, factor out ${10}^6$, and then add the quantities in parentheses together. Once there, you can use exponent rules to simplify your equation. Divide through and multiply by $100$ to get the RBC component as a percentage. Work is shown below.
$RBC=\frac{5.4\times {10}^6}{5.4\times {10}^6+7.5\times {10}^3+3.5\times {10}^5}$
$RBC=\frac{5.4\times {10}^6}{5.4\times {10}^6+0.0075\times {10}^6+0.35\times {10}^6}$
$RBC=\frac{5.4\times {10}^6}{{10}^6(5.4+0.0075+0.35)}$
$RBC=\frac{5.4}{5.7575}$
Note that the answer choices are, for the most part, par apart. Because $5.4$ is relatively close to $5.7575$, you can conclude with confidence that the correct answer is likely close to $100$%. Therefore, (D) is the correct answer. If this question is in the calculator section, you can plug the numbers into your calculator to check:
% $RBC=\frac{5.4}{5.7575}\times 100\approx 93.79$%
Choice (D) is still correct.