Duplicate, triplicate, sub-duplicate, sub-triplicate, compounded ratios
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Two numbers are in the ratio 2 : 3. If 5 is added to each number, the ratio becomes 5 : 7. Find the numbers.
if `x/a = y/b = z/c` prove that `(ax - by)/((a + b)(x - y)) + (by - cz)/((b + c)(y - z)) + (cz - az)/((c + a)(z - x)) = 3`
A school has 630 students. The ratio of the number of boys to the number of girls is 3 : 2. This ratio changes to 7: 5 after the admission of 90 new students. Find the number of newly admitted boys.