Dividing money

The father originally wanted to divide the financial amount between his sons in the ratio of 7:6. However, he then split it at 6:5 (in the same order). One of the sons got angry that he should have received 120 euros more. How many euros did each son receive?

Final Answer:

a =  9360 Eur
b =  7800 Eur

Step-by-step explanation:

$$\begin{gathered} \frac{7}{7+6}\cdot x+120=\frac{6}{6+5}\cdot x \\ ((7)/(7+6))\cdot x+120=((6)/(6+5))\cdot x \\ 0.006993x=120 \\ x=\frac{120}{0.00699301}=17159.99999998 \\ x=17160 \\ a=\frac{6}{6+5}\cdot x=\frac{6}{6+5}\cdot 17160=9360\text{Eur} \end{gathered}$$

$$\begin{gathered} b=\frac{5}{6+5}\cdot x=\frac{5}{6+5}\cdot 17160=7800=7800\text{Eur} \\ \text{ Verifying Solution: } \\ X=a:b=9360:7800=\frac{6}{5}=1.2=6:5\text{eur} \\ X=x \\ r=a/b=9360/7800=\frac{6}{5}=1.2 \end{gathered}$$

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