Answer:
Jan is 10 years old.
Kate is 30 years old.
Step-by-step explanation:
To solve this problem, we need to find a system of equations.
Now: Kate is three times as old as Jan.
This statement can be expressed as [tex]K=3J[/tex], beacuse "three times" indicates a product.
6 years ago: She was six times as old as he was.
This statement can be expressed as [tex]K-6=6(J-6)[/tex], notice that we had to subtract 6 units, representing 6 years in the past.
Let's replace the first equation into the second one
[tex]3J-6=6(J-6)\\3J-6=6J-36\\-6+36=6J-3J\\3J=30\\J=\frac{30}{3}\\ J=10[/tex]
Therefore, Jan is 10 years old.
Then, [tex]K=3J \implies K=3(10)=30[/tex]
Therefore, Kate is 30 years old.
