Larry is 4 years older than Moe. Nine years ago, Larry was 5 times as old as Moe was then. How old is each now?

Question

im not exactly sure how to set up an equation for this. i'm not sure where to put x and how to write the equation. 

Answer 1

Larry's today's age =x

Moe today's age =y

"Larry is 4 years older than Moe"
x = y +4      equation 1

"Nine years ago, Larry was 5 times as old as Moe was then."

Nine year ago Larry's age = x-9

Nine year ago Moe's age =y-9

x-9 =5(y-9)   equation 2

Now substitute equation 1 , x=y+4   in equation 2  ,  x-9=5(y-9)

 

x -9 =5(y-9)

y+4-9=5y -45

 

y-5 =5y -45

 

40 = 4y

 

10 = y

 

Substitute  y=10 in equation 1 x=y+4

 

x = y+4

x =10+4 =14

 

 

Larry's today's age =x=14
Moe today's age =y=10