Maths - Two numbers are such that the ratio between then is 4:7. if each is increased by 15. the?

The Question can be formulated as:
(4x+15) / (7x+15)=7 / 11
After some rearranging you find -- ehm, OK, we'll do this step by step:

First, multiply both sides by a polynomial to clear fractions:
11(4x+15)=7(7x+15)
Write the linear polynomials on both sides in standard form:
44x+165=49x+105
Isolate x to the left hand:
- 5x= - 60
Solve for x by dividing both sides by -5:
x=12

When it comes to verifying, plug in this 12 into the formula above:

(4 * 12)) / (7 * 12) = 48 / 84 with a ratio of 4:7.
Add 15 to both, you get:
(48+15) / (84+15) = 63 / 99 with a ratio of 7:11.