SOLUTION: Rex is 30 years younger than his father. His mother is three times as old as her son. Find Rex's age if his father is two years older than his mother?

Question 105578: Rex is 30 years younger than his father. His mother is three times as old as her son. Find Rex's age if his father is two years older than his mother?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let the age of Rex's father be F.
.
Then Rex's age (30 years younger than his father) is F - 30.
.
Rex's mother is 3 times as old as Rex. So her age is 3 times Rex's age or 3(F - 30).
.
Rex's father's age (which is F) is two years more than his mother's age (which is 3(F - 30).
So if you take 2 years from his father's age, the result will equal his mother's age. In
equation form this is:
.
F - 2 = 3(F - 30)
.
Multiply out the right side and you have:
.
F - 2 = 3F - 90
.
Get rid of the 2 on the left side by adding 2 to both sides:
.
F = 3F - 88
.
Eliminate the 3F on the left side by subtracting 3F from both sides to make the equation
become:
.
-2F = -88
.
Solve for F by dividing both sides by -2 and you have:
.
F = -88/-2 = 44
.
So Rex's father is 44 years old. Since Rex is 30 years younger than that, Rex is 44 - 30 or 14
years old. And since Rex's mothers age is 3 times Rex's age, his mother is 3 times 14 or
42 years old. Notice that Rex's father is two years older than Rex's mother, so the problem
checks.
.
In summary ... Rex's age is 14.
.
Hope this helps you to understand the problem.
.
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