SOLUTION: Manuel is 43 years old. Delaney is 30 years old. How many years ago was Manuel's age 2 times Delaney's age?

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Manuel is 43 years old. Delaney is 30 years old. How many years ago was Manuel's age 2 times Delaney's age?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1146709: Manuel is 43 years old. Delaney is 30 years old. How many years ago was Manuel's age 2 times Delaney's age?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
m, Manuel
d, Delaney
x, how many years ago
p, factor
-
-

m-x=p%28d-x%29
-
m-x=pd-px
m-pd=x-px
pd-m=px-x
%28p-1%29x=pd-m
highlight_green%28x=%28pd-m%29%2F%28p-1%29%29
Make the substitutions system%28m=43%2Cd=30%2Cp=2%29.

Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.

First, easy mental solution 


    The difference between their ages is 43-30 = 13 years.


    Hence, Manuel was two times Delaney age, when they were 26 (Manuel) and 13 (Delaney years old.


    It happened 30 - 13 = 17 years ago.


Next, easy Algebra solution 

    Let x be "how many years ago", i.e, the unknown value under the question.


    Then you have this "age" equation


        43 - x = 2*(30-x).


    Simplify and solve for x.


        43 - x = 2*30 - 2x

        2x - x = 2*30 - 43

         x     = 60 - 43 = 17,


    and you have the same answer.