The inheritance

Dad initially decided to bequeath the money to his two sons so that they would share it 8:7 (older and younger). Then, he changed his mind and divided the same amount into a ratio of 11:9 (older and younger). This step increased the inheritance value for the older son by 925 tolars.

How much did the father send to both sons together?

Correct answer:

x =  55500

Step-by-step explanation:

$$\begin{gathered} \frac{8}{8+7}\cdot x+925=\frac{11}{11+9}\cdot x \\ \frac{8}{15}\cdot x+925=\frac{11}{20}\cdot x \\ 8\cdot 20\cdot x+15\cdot 20\cdot 925=15\cdot 11\cdot x \\ 160x+277500=165x \\ 5x=277500 \\ x=277500/5=55500 \end{gathered}$$

Try another example