Mathematics: If now Kate is three times as old as Jan, and 6 years ago she was six times as old as he was, how old are they now?

the missing piece is 9Step-by-step explanation:...

If now Kate is three times as old as Jan, and 6 years

Kakey1668

27.01.2022

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 K=3J , beacuse "three times" indicates a product.

6 years ago: She was six times as old as he was.

This statement can be expressed as K-6=6(J-6) , notice that we had to subtract 6 units, representing 6 years in the past.

Let's replace the first equation into the second one

$3J-6=6(J-6)\\3J-6=6J-36\\-6+36=6J-3J\\3J=30\\J=\frac{30}{3}\\ J=10$

Therefore, Jan is 10 years old.

Then, $K=3J \implies K=3(10)=30$

Therefore, Kate is 30 years old.

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