The larger of two numbers is eight more than three times the smaller number. the sum of the two numbers is fifty-two. find the two numbers.

So... we have two numbers
say "a" and "b"

one is larger than the other, let us say, "b" is larger than "a"
by how much?
well, "eight more than three times"
three times the smaller is 3 * a, or 3a
eight more than that is 3a + 8

so b = 3a+ 8
the sum of both of them is 52
so, we know that

a + b = 52

run a substitution on "b" on the 2nd equation, and solve for "a"
once you find "a", plug it back in the 2nd equation, to get "b"