Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as daniel.

Question

How old is daniel now?

Answer 1

K will represent Kevin's age. D will represent Daniels age.

Kevin is 3 years older than Daniel So K = 3 + D

Two years ago, Kevin's age was K-2 and Daniels age was D - 2. So we use these to write an expression for their ages 2 years ago.

"2 years ago, Kevin was 4 times as old as Daniel." becomes K-2 = 4*(D-2)

that is Kevin 2 years ago was 4 times Daniels age 2 years ago.

Distribute the 4 into the (D - 2) and get K - 2 = 4D - 8

Also we know from above that K = 3 + D, so replace K with 3 + D

K - 2 = 4D - 8 becomes 3 + D - 2 = 4D - 8

Now solve. Put all D's on the left and all constants on the right. Start by subtracting D from both sides.

3 - 2 = 4D - 8 - D or 1 = 3D - 8

Now add 8 to both sides

1+8 = 3D or 9 = 3D Now divide both sides by 3 and find that Daniel is 3 years old. (Kevin is 6 years old)

2 years ago Daniel was 1 and Kevin was 4 and Kevin's age was 4 times Daniel's.

So the answer is that Daniel is 3 years old.