SOLUTION: Ten years ago, Pepito's age was three times the age of his son, Chito. After ten years, Pepito’s age will be twice that of his son. Find the ratio of their present ages

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Question 1204000: Ten years ago, Pepito's age was three times the age of his son, Chito. After ten years, Pepito’s age will be twice that of his son. Find the ratio of their present ages
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
p Pepito
c Chito

You could start this way: .

-----------------------
Find the ratio of their present ages
-----------------------



E2-E1:


Using E2:




Ratio, .
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Ten years ago, Pepito's age was three times the age of his son, Chito.
After ten years, Pepito’s age will be twice that of his son. Find the ratio of their present ages
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let C be the Chito's age; P be the Pepito's age.


Then for their ages 10 years ago we have

    P-10 = 3(C-10)

or  P = 3(C-10) + 10 = 3C -20.    (1)



For their ages in ten years, we have this equation

    P + 10 = 2(C+10),

or  P = 2C + 10.                  (2)



From (1) and (2), we have

    3C - 20 = 2C + 10,

    3C - 2C = 20 + 10,

       C    =   30.


So, the son is 30 years old; the father is 3C - 20 = 3*30 - 20 = 70.


The ratio of their ages is  P/C =  = .    ANSWER

Solved.



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


You have received two responses showing valid solutions using two variables.

Often the actual algebra required to solve the problem is easier if you can set the problem up using a single variable. Let's see what happens if we do that.

Let x = Chito's age 10 years ago
Then 3x = Pepito's age 10 years ago

Chito's age 10 years from now will be x+20; Pepito's age then will be 3x+20. At that time, Pepito's age will be twice Chito's age:





10 years ago, Chito's age was x=20 and Pepito's age was 3x=60.

So now their ages are x+10 = 30 and 3x+10 = 70.

ANSWER: the ratio of their ages is 30:70, or 3:7 (or 7:3)
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