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Julio is 36 years old and James is 11 years old. In how many years will Julio's age be twice James age?

I just watched someone solve this problem and I don't understand how this person got the answer that she got.
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5 Answers

Hello Amie,
If we call the number of years we are looking forward x, then we can state the problem this way:
Julio's age plus some number of years is double James' age plus the same number of years.
Then we just have to solve for x.
36+x=22+2x         distribute
14+x=2x               subtract 22 from each side
14=x                     subtract x from each side
We have that x is 14 years.  This makes sense because in 14 year, Julio will be 50 and James will be 25.
Another way of looking at the question (and getting around the algebra) is this: Julio was 25 years old when James was born (36-11=25).  So when James hits 25, Julio will be twice his age.  James is 11, so that will happen in 14 years.
To check: In 14 years, James will be 11+14 (25).  Julio will be 36+14 (50).  
Let y represent the number of years that will be added to each age to find their age in the future. You can set up a table if you want.
                             age now                           age in future
Julio                           36                                   36+y
james                         11                                   11+y       
Now lookat the next sentence and translate that into an equation .
Julio's age is twice James' age.
36+y         = 2(11+y)
36+y          = 22 + 2y
     -y                    - y
36                        = 22 + y
-22                          -22 
14                         =     y
Check the answer and make sure you're answering the right question. According to this, in 14 years julio will be twice james age. From our table under future age, Julio will be 50 and james will be 25, so our answer works.
So our answer. is 14 years.
Let x = number of years    11 + x = James' age in the future     36 + x = Julio's age in the future
36 + x  = 2(x + 11)     because Julio's age will be twice James' age at some amount of time in the future
36 + x = 2x + 22        using the distributive property
      14 = x                 subtract 22 from both sides and subtract x from both sides
Thus, in 14 years, James will be 25 and Julio will be 50, twice James's age.
Let x = the number of years that Julio will be twice James' age.  In x years, we want:
2* (James' age) = Julio's Age
2*(11+x) = 36+x
22 + 2x = 36 + x
Solve for x