Question 572723
Melinda's mother is four times as old as Melinda. In 16 years, her mother will twice her age. How old is melinda now?


Let's use X and Y to mean Melinda's age (X) and her mom's age (Y) today. 
Melinda's mom is 4 times Melinda's age.  So Y = 4X
In 16 years, Melinda will be X+16 and her mom will be Y+16.  At that time Melinda's mom will be 2 times Melinda's ago.  So if we double Melinda's age at that time, 2(X+16) that will equal Melinda's mom age at that time (Y+16).


Now, put these together.  We need to solve for one variable - Melinda's age X.


Y=4X
2(X+16)=Y+16
Substituting for Y:
2(X+16) = (4X)+16
2X + 32 = 4X + 16.  Subtract 2X from each side ... 
32 = 2X +16.  Subtract 16 from each side ... 
16 = 2X.   Divide both sides by 2 ... 
8 = X.
So, going back to the original problem, Melissa is 8.  


Now, let's check.
If Melinda is 8, then her mom is 4 time 8 = 32.
In 16 years, Melinda will be 8+16 = 24.  
In 16 years, Melinda's mom will be 32+16 = 48.
Will her mom be 2 time Melinda's age then? 
24 * 2 = 48.  Correct!