Question 824453: Raja's age is one fifth his father's age.After 6 years,his age will be one third his father's age.How old are they now. Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! Let r = Raja's age and
let f = father's age
In six years they will both be six years older. So
r + 6 = Raja's age in 6 years
f + 6 = father's age in 6 years
With two variables we will need two equations. "Raja's age is one fifth his father's age" translates into:
And "After 6 years,his age will be one third his father's age" translates into:
(Note the use of parentheses. This is critical when using multiple term expressions, like f+6, to express a single value (the father's age in 6 years). In this case it helps us see that the 1/3 should be distributed.)
Now that we have two equations we can solve. There are many methods to solve a system like:
One of these methods is called the Substitution Method and, since the first equation is already solved for r, this appears to be the easiest method for this system. Substituting for r in the second equation we get:
(Again with the parentheses! It just a good idea to use them any time you make substitutions.) Now we solve for f. We start by simplifying each side:
Multiplying each side by 15 (the lowest common denominator of 3 and 5) in order to eliminate the fractions:
Get the variable on one side (by subtracting 3f):
Subtracting 30:
Divide by 2:
Looking back we can see "let f = the father's age". So the father is 30 years old.
The problem asks for both of their ages. So we need to use the solution we got for f and one of the two-variable equations to find r. Let's use
Substituting in the value we got for f:
Simplifying:
So Raja's current age is 6 and the father's age is 30.
P.S. As a check, we could see if the other equation, , works for these values for r and f: Check!
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