Question

Kevin is 3 times as old as Daniel. 4 years ago, Kevin was 5 times as old as Daniel.
How old is Kevin 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.

hope u like it :)

Answer 2

Daniel is D

Kevin is K

K = 3D

(K-4) = 5(D-4)

K-4 = 5D - 20

= 20 - 4 = 5D - K

Using the equation K = 3D

Since K is the same as 3D

5D - 3D = 20 - 4

2D = 16

D is 8

So since K = 3D

K = 3(8)

K = 24

So Kevin is 24.