Nelson is twice as old as Maria. Six years ago, Nelson was 5 times as old as Maria. How old was Nelson 6 years ago?

Question

Nelson is twice as old as Maria.  Sic years ago, Nelson was 5 times as old as Maria.  How old was Nelson six years ago.  I need the formula for this problem and the solution.

 

Answer 1

Gloria,

 

You need to set up a system of equations to solve this since there are two variables: Nelson's age and Maria's age.

 

Let x be Nelson's age and y be Maria's age.  Then, we know from the description that:

 

(1) Nelson is twice as old as Maria => x = 2y

 

Also, we know that:

 

(2) 6 years ago, Nelson was 5 times older than Maria => x - 6 = 5(y - 6) - remember, x & y are their ages now.

 

Since we have two equations and two variables, we can use substitution to solve.

 

Substitute the value of x in (1), 2y for the value of x in (2):

 

2y - 6 = 5(y - 6)

 

Distribute the right side:

 

2y - 6 = 5y - 30

 

Subtract 2y from both sides and add 30 to both sides:

 

24 = 3y

 

Divide both sides by 3:

 

8 = y (Maria's age)

 

To find Nelson's age, use this value of y in (1):

 

x = 2*8 = 16 (Nelson's age now)

 

Six years ago, Nelson was 16 - 6 = 10 years old.

 

Hope this helps!