Thanks 81022

Pavla is 2x older than Irena. Four years ago, Pavla was 6 times older than Irena was then. In how many years will the ages of Pavla and Irena be in the ratio of 4:3? Thanks

Correct answer:

x =  10

Step-by-step explanation:

$$\begin{gathered} p=2i \\ p-4=6(i-4) \\ p=2\cdot i \\ p-4=6\cdot (i-4) \\ 2i-p=0 \\ 6i-p=20 \\ Pivot:Row1\leftrightarrow Row2 \\ 6i-p=20 \\ 2i-p=0 \\ Row2-\frac{2}{6}\cdot Row1\to Row2 \\ 6i-p=20 \\ -0.67p=-6.67 \\ p=\frac{-6.66666667}{-0.66666667}=10 \\ i=\frac{20+p}{6}=\frac{20+10}{6}=5 \\ i=5 \\ p=10 \\ (p+x):(i+x)=4:3 \\ 3\cdot (p+x)=4\cdot (i+x) \\ 3\cdot (10+x)=4\cdot (5+x) \\ x=10 \\ x=\frac{10}{1}=10 \\ x=10 \end{gathered}$$

Try another example