Kate’s age 5 years ago, doubled, is equal to triple her age 10 years ago

Answer 1

Let K be Kate's age now

So K-5 will be Kate's age 5 years ago

And K-10 will be Kate's age 10 years ago

To double her age five years ago we write it as

2(K-5)

To triple her age ten years ago we write it as

3(K-10)

the problem says they are equal so we set them equal and solve for K

2(K-5)=3(K-10)

Distribute

2K-10=3K-30

Subtract 2K from each side

-10=K-30

Add 30 to both sides

20=K

Kate is now 20 years old.

Five years ago she was 15 and ten years ago she was 10.