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a geologist had two rocks on a scale that weighed 2 1/2 pounds together rock A weighed a total of 1/7 of the weight how much did rock A weigh

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It is already given in the question that the combined weight of two rocks is  2 /1/2 pounds. The weight of rock A is also known and it is 1/7 of the total weight of the two rocks. This is enough to find the desired solution.
Now
Total weight of the two rocks = 2 1/2 pounds
                                               = 5/2 pounds
Then
Weight of Rock A = (5/2)/(1/7) pounds
                             = (5 * 7)/2 pounds
                             = 35/2 pounds
                             17 1/2 pounds
So Rock A weighs 17 1/2 pounds. This is the weight of Rock A and it is only required for this question. If you are eager to find the weight of rock B then you have to subtract the weight of Rock A form the total weight of the two rocks.

Answer:

Let A and B be the two rocks.

As per the statement: a geologist had two rocks on a scale that weighed 2 1/2 pounds together rock

⇒Total weight of rock (\(A+B\)) = \(2\frac{1}{2}\) pounds

or

\(A+B= \frac{5}{2}\)

Also, it is given A weighed a total of \(\frac{1}{7}\) of the weight.

⇒ \(A = \frac{1}{7} \times (\text{Total weight})\)

then;

\(A = \frac{1}{7} \times \frac{5}{2} = \frac{5}{14}\)

Therefore, \(\frac{5}{14}\) pounds did rock A weight.

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