Ratio of two unknown numbers

Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?

Correct result:

a =  12
b =  18

Solution:

a+b=30
a+(b/6) = 5/7 •(b+b/6)

a+b = 30
42a-28b = 0

a = 12
b = 18

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