Let's call the two numbers a and b. Three options here:
-choose numbers for a and b. Work out s, p and q, and plug these into each answer. If only one answer gives you your numbers a and b, it must be right. If two answers both give you the right numbers a and b, try again.
-we know the two numbers add to s. Well, try adding the numbers in each answer choice - the right answer has to give you s. Only D does.
-do the algebra:
a + b = s
a/b = p/q
So a = s - b, and a = pb/q, so s-b and pb/q must be equal:
pb/q = s - b
pb/q + b = s
b(p/q + 1) = s
b = s/[p/q + 1]
b = sq/(p + q)
from which D must be correct (no need to find a).
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