Adam is 3 times as old as Cynthia and Fred is 16 years younger than Adam. One year ago, Adam's age was twice the sum of Cynthia's and Fred's age. Find their present age:
(Write answer as Adam is __, Cynthia is __, Fred is __)
Cyntia --- x
Adam ---- 3x
Fred ----- 3x - 16
one year ago:
Cyntia --- x-1
Adam ---- 3x-1
Fred ----- 3x - 17
at that time "Adam's age was twice the sum of Cynthia's and Fred's age"
---> 3x-1 = x-1 + 3x-17
solve for x
check that your answer meets the conditions
To solve this problem, we need to use algebraic equations to represent the given information and then solve for the unknowns. Let's assume the present age of Cynthia is x.
Given that Adam is 3 times as old as Cynthia, we can write: Adam = 3x.
And it is also given that Fred is 16 years younger than Adam, so we can write: Fred = Adam - 16.
Now, let's consider the information about their ages one year ago. One year ago, Adam's age was Adam - 1, Cynthia's age was x - 1, and Fred's age was Fred - 1.
According to the problem, Adam's age one year ago was twice the sum of Cynthia's and Fred's age. So we can write the equation: Adam - 1 = 2 * (Cynthia - 1 + Fred - 1).
Let's substitute the values we obtained earlier for Adam and Fred into this equation: 3x - 1 = 2 * (x - 1 + (3x - 16) - 1).
Simplifying the equation: 3x - 1 = 2 * (x - 1 + 3x - 17).
Further simplification gives: 3x - 1 = 2 * (4x - 18).
Expanding the right side of the equation: 3x - 1 = 8x - 36.
Bringing the x terms to one side and the constant terms to another side: 8x - 3x = 36 - 1.
Combining like terms: 5x = 35.
Divide both sides by 5 to solve for x: x = 7.
Now we know that Cynthia's present age is x = 7. Using this, we can find the ages of Adam and Fred.
Adam = 3 * x = 3 * 7 = 21.
Fred = Adam - 16 = 21 - 16 = 5.
So, the present ages are: Adam is 21, Cynthia is 7, and Fred is 5.