Question 909376: Five years ago, Sam was four times as old as John, and in five years he will
be twice as old as John. Find the present ages of each.
Answer by FaroukHarb(6)   (Show Source):
You can put this solution on YOUR website! Let x be The age of Sam TODAY
Let y denote the age of John TODAY
Five years ago, Sam was four times as old as John
This simply translates that 4 years ago from their CURRENT age, Sam's age back then was 4 times john's age which translates in algebra to:
(x - 4) = 4(y - 4)
simplifying:
x - 4 = 4y - 16
x - 4y = -12 (*)
Now for the next part,
and in five years he (refers to sam) will be twice as old as John
This is again the same concept, after 5 years, Sam's age will now equal to 2 times the age of john's which in algebra translates to:
(x + 5) = 2(y + 5)
x + 5 = 2y + 10
x - 2y = 5 ($)
Now we have two equations, (*) and ($) Which are:
x - 4y = -12 (*)
x - 2y = 5 ($)
If we subtract (*) from ($) we get:
-2y = -17
y = 17/2
y = 8.5 years old
Therefore John's current age is 8.5 years (Technically he is still 8 years old)
Solving for x we get:
x - 4y = -17
x - 4(8.5) = -17
x - 34 = -17
x = 17
Terefore Sam's current age is 17
Hope it helped,
El Farouk
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