Question

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

Answer 1

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 2

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(1)/(2)` pounds

or

`A+B= (5)/(2)`

Also, it is given A weighed a total of
`(1)/(7)` of the weight.

⇒
`A = (1)/(7) * (\text{Total weight})`

then;

`A = (1)/(7) * (5)/(2) = (5)/(14)`

Therefore,
`(5)/(14)` pounds did rock A weight.