I need the algebra sentence for the following problem..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.
Let Adam=x, Cynthia=y and Fred=z
We have: x=3y, z=x-16 , x-1=2(y-1+z-1)
so x=3y, x=z+16 and x=2y+2z-3
3y=z+16 so z=3y-16
Also,
3y=2y+2z-3 so y=2z-3 = 2(3y-16)-3=6y-35 so 5y=35 and y=7, z=3(7)-16=5 and x=3(7)=21
To solve this problem algebraically, we can assign variables to each person's age. Let's use A for Adam's age, C for Cynthia's age, and F for Fred's age.
Given:
1. Adam is 3 times as old as Cynthia: A = 3C
2. Fred is 16 years younger than Adam: F = A - 16
3. One year ago, Adam's age was twice the sum of Cynthia's and Fred's age: (A - 1) = 2((C - 1) + (F - 1))
To find their present ages, we need to solve this system of equations simultaneously. Let's substitute the values from equation 1 and equation 2 into equation 3.
Substituting A = 3C and F = A - 16 into equation 3:
(3C - 1) = 2((C - 1) + ((3C) - 16 - 1))
Now simplify and solve for C:
3C - 1 = 2(C - 1 + 3C - 17)
3C - 1 = 2C - 2 + 6C - 34
3C - 1 = 8C - 36
36 - 1 = 8C - 3C
35 = 5C
C = 35/5
C = 7
Now that we know Cynthia's age, we can substitute this value into equation 1 to find Adam's age:
A = 3C
A = 3(7)
A = 21
Finally, we can substitute Adam's age into equation 2 to find Fred's age:
F = A - 16
F = 21 - 16
F = 5
Therefore, their present ages are:
Adam is 21 years old, Cynthia is 7 years old, and Fred is 5 years old.