SOLUTION: My Age: 39 Elijah: 12 At some point , my age will be 3 times Elijah's age. Is this correct: 3x= 3(x-27) How do I solve? Thanks!

Question 592692: My Age: 39
Elijah: 12
At some point , my age will be 3 times Elijah's age.
Is this correct:
3x= 3(x-27)
How do I solve?
Thanks!
Answer by ntnk(54) (Show Source): You can put this solution on YOUR website!
The equation you have written is not quite correct. Let's see how to solve it before getting to the age question.

First we use the distributive property on the right-hand side to get

Then we subtract 3x from both sides to get

which is obviously false, so that means the equation above does not have a solution.
Let's think about what the problem is telling us. Right now you are 39 and Elijah is 12. Next year, you will be 40 and Elijah will be 13. The year after that, you will be 41 and Elijah will be 14.
More generally, in X years, your age will be 39 + X and Elijah's age will be 12 + X. (For example, if we plug in X=1 or X=2, we get the statements from the previous paragraph.)
We want to know when your age will be three times Elijah's age. So we take three times Elijah's age:
3 * (12 + X)
and set it equal to your age: (39 + X). This gives the equation

We use the distributive property on the left hand side to get

Now subtract X from both sides to get

Then subtract 36 from both sides to get

and finally divide by 2 to get

Now we can check the final answer. In 1.5 years, you will be 39+1.5 = 40.5 years old, and Elijah will be 12+1.5 = 13.5 years old. Indeed, in 1.5 years you will be 3 times older than Elijah since
13.5 * 3 = 40.5
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