SOLUTION: John is 6 years older than James. In 5 years John will be 3 times as old as James was 3 years ago. What are their present ages?

Question 1089890: John is 6 years older than James. In 5 years John will be 3 times as old as James was 3 years ago. What are their present ages?
Answer by EMStelley(208) (Show Source): You can put this solution on YOUR website!
Let's start by declaring variables for both John's age and James' age.
Let X = John's age
Let Y = James's age
The first sentence is "John is 6 years older than James." 6 years older can be represented with addition. So if we translated this into an equation we would get:

The second sentence is more complicated. "In 5 years" can be represented with addition, "John will be" implies an equal sign, "3 times as old" implies multiplication, and "3 years ago" implies subtraction. Putting this all together, we get:

If we solve this second equation for X just like the first one, we get:

Now we have two equations, and two unknowns (X, Y), so we need to solve for both of these variables. There are many methods that can be used here, but in this case, I think the easiest one is to set the two equations equal to each other. Why does this work? Because both equations are X = . So the other side of each equation must be the same because they are both equal to X. So we have:

Solving this for Y lends:

Now we know Y = 10. In other words, James is currently 10 years old. To find John's age, we can use either of the two equations we started with. Since the first one is simpler, let's use that one. If Y is 10, and X is 6 + Y, then X would be 16. In other words, John is currently 16 years old.
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