Answer:
Ali is 14 years old.
Ali's dad is 36 years old.
Explanation:
We can find Ali and her dad's ages using a system of equations, where:
- A represents Ali's current age,
- and D represents her dad's current age.
----------------------------------------------------------------------------------------------------------First equation:
Since the sum of Ali and her dad's ages is 50, our first equation is given by:
A + D = 50
Second equation:
Since Ali's dad will be twice as old her in 8 years, our second equation is given by:
2(A + 8) = D + 8
Method to solve: Substitution:
First, let's isolate A in the first equation:
(A + D = 50) - D
A = -D + 50
Solving for D:
Now, we can solve for D by substituting -D + 50 for A in the second equation in our system:
2(-D + 50 + 8) = D + 8
2(-D + 58) = D + 8
(-2D + 116 = D + 8) - 8
(-2D + 108 = D) + 2D
(108 = 3D) / 3
36 = D
Thus, Ali's dad is currently 36 years old.
Solving for A:
Now, we can solve for A by plugging in 36 for A in the first equation in our system:
(A + 36 = 50) - 36
A = 14
Thus, Ali is currently 14 years old.
Checking the validity of the answer:
- From our first equation, we know that 14 + 36 is indeed 50, so the solutions are correct for this equation.
- From our second equation, we know that Ali's dad will be 44 in 8 years, while she will be 22 in 8 years. Because 44 is twice 22, the solutions are also correct for this equation.