SOLUTION: Jamar is 4 times as old as Josh. In 20 years he will be twice as old as Josh. How old is Jamar ?

Question 3407: Jamar is 4 times as old as Josh. In 20 years he will be twice as old as Josh. How old is Jamar ?
Answer by drglass(89) (Show Source): You can put this solution on YOUR website!
The idea with a problem like this is to rewrite the question in mathematical terms. Let's call Jamar's age right now x and Josh's age right now y. We don't know either of these values, but we want to figure out Jamar's age, which we call x.

Now let's describe the facts mathematically

First, Jamar is 4 times as old as Josh, mathematically, this is

Second, in 20 years, Jamar will be twice as old as Josh. Jamar's age in twenty years is his age now plus 20, likewise, Josh's age in twenty years is his age now plus 20 years. We can write the second fact as

This gives us two facts:

subtract 20 from both sides of the second equation to get

substitute the equation for x in the first equation for x in the second equation to get

subtract 2y from both sides of the equation

divide both sides by 2 to get .

This means Josh's age right now is 10, since Jamar is 4 times as old as Josh, so Jamar's age right now is 40. In twenty years, Jamar will be 60 (40 + 20) and Josh will be 30 (10 + 20) 60 is twice as much as 30. So this answer works.
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