What are the ages of Jess, her son and her mom right now?

Question

The ratio of Jess's age to her mom's age is now 6:11. The ratio of Jess's age to her sons Henry's age is 1:12. In 4 more years, the total of all ages (Jess, Jess's mom and Jess's son) will be 117. What are the ages of Jess, her son and her mom right now? 

Answer 1

J=Jesse

M=Mom

S=Son

 

J/M=6/11

J/S=12/1  (it can't be 1/12)

J/M=6/11=12/22 (because the ratio of Jesse to Son is 12/1)

x=the number you have to multiply the terms of the ratios by to get the ages

J/M=12x/22x

J/S=12x/1x

in 4 years...

J/M=(12x+4)/(22x+4)

J/S=(12x+4)/(x+4)

(12x+4) is Jesse's age (don't count Jesse's age twice)

(22x+4)=Mom's age

(x+4)=Son's age

the sum of their ages is 117

(12x+4)+(22x+4)+(x+4)=117

35x+12=117

35x=117-12

35x=105

x=105/35

x=3, the multiplier

12x=12*3=36 years old for Jesse

22x=22*3=66 years old for Mom

x=3 years old for Son

 

Answer 2

Mom 66   Jess 36    Son 3

 

 

70              +40          +7   =    117

 

 

(I did this in i5 seconds before I went to bed - sorry it's so short)