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------------------------------------------------ The average blue whale weighs 300,000 pounds (136,000 kilograms). The average man is [tex]\frac{1}{1,818}[/tex] the weight of a blue whale. How much does the average man weigh in pounds?

Select one of the following:

A. [tex]165 \frac{5}{303}[/tex] lbs
B. [tex]205 \frac{3}{890}[/tex] lbs
C. [tex]242 \frac{7}{425}[/tex] lbs
D. [tex]234 \frac{7}{303}[/tex] lbs

Answer :

We start with the fact that the average blue whale weighs
[tex]$$300,\!000 \text{ lbs},$$[/tex]
and that the average man weighs
[tex]$$\frac{1}{1818}$$[/tex]
of a blue whale's weight. Therefore, the man's weight in pounds is given by

[tex]$$\text{Man's weight} = \frac{300,\!000}{1818}.$$[/tex]

To write this result as a mixed number, we first perform the division to obtain the whole number part.

1. Divide 300,000 by 1,818. The integer part (quotient) is 165 since

[tex]$$165 \times 1818 = 299970.$$[/tex]

2. Next, find the remainder by subtracting:

[tex]$$\text{Remainder} = 300,\!000 - 299970 = 30.$$[/tex]

3. This remainder represents the fractional part of the weight as

[tex]$$\frac{30}{1818}.$$[/tex]

4. Now, simplify the fraction [tex]$\frac{30}{1818}$[/tex]. The greatest common divisor (GCD) of 30 and 1818 is 6. Dividing the numerator and denominator by 6 gives

[tex]$$\frac{30 \div 6}{1818 \div 6} = \frac{5}{303}.$$[/tex]

Thus, the average man's weight is

[tex]$$165 \frac{5}{303} \text{ lbs}.$$[/tex]

This is the final answer.