2 Answers

Conor Cosnett · Answer 1 · 2021-12-09T15:46:40+0000

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 , beacuse "three times" indicates a product.

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

This statement can be expressed as , notice that we had to subtract 6 units, representing 6 years in the past.

Let's replace the first equation into the second one

Therefore, Jan is 10 years old.

Then,

Therefore, Kate is 30 years old.

Sean Kinsey · Answer 2 · 2021-12-12T03:14:00+0000

Answer:

Jan is 10 years old.

Explanation:

To solve this problem, we need to find a system of equations.

This statement can be expressed as
K=3J , beacuse "three times" indicates a product.

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

$3J-6=6(J-6)\\3J-6=6J-36\\-6+36=6J-3J\\3J=30\\J=(30)/(3)\\ J=10$

Therefore, Jan is 10 years old.

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

Therefore, Kate is 30 years old.