Jack is 2 times as old as Lacy. 6 years ago the sum of their ages was 18. How old are they now?

Question

Jack is 2 times as old as Lacy. 6 years ago the sum of their ages was 18. How old are they now?

Answer 1

for this one, we need to assign either jack or lucy to a variable

 

since jack is 2 times older than lucy it is easier math to assign lucy to a variable.

 

so we say

 

lucy = x

 

now we set up our equation

 

if we know that 6 years ago their ages were 18 combined, then we know that something - 6 = 18

 

since we also know that jack is 2 times lucy now

 

then the entire formula would be

 

2x - 6 = 18

 

to solve we add 6 to both sides

 

2x - 6 + 6 = 18 + 6

 

the 6s on the left cancel because when you have a positive and negative of the same number it always = 0

 

we get

 

2x = 24

 

then divide both sides by 2 to get the answer

 

2x / 2 = 24 / 2

 

the 2s on the left cancel and you get

 

x = 12

 

then answer is 12