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

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.