Jeff is 4 times older than his daughter. Five years ago he was 9 times older than his daughter. Write an algebraic equation to determine the age of his daughter.

Jeff is 32, His Daughter is 8

The relationship between the age of Jeff and his daughter can be summarized by the following systems of equation:

Jeff's age = x

Jeff's Daughter's age = y

x=4y    jeffs age is equal to his daughters times four

x-5=9(y-5) jeffs age minus five is equal to his daughters age minus five as well times 9

Combining these equations will get us x=32, y=8.

The algebraic equation 4D - 5 = 9D - 45. The current age of Jeff's daughter is 8 years old.

Let's represent the current age of Jeff's daughter as "D" and Jeff's current age as "J".

According to the problem:

Jeff is 4 times older than his daughter, so we can express this relationship as:

J = 4D

Five years ago, he was 9 times older than his daughter. This means that their ages five years ago are:

(J - 5) = 9(D - 5)

Now, we can write the algebraic equation to determine the age of his daughter (D):

(J - 5) = 9(D - 5)

Since we already know that J = 4D, we can substitute this into the equation:

(4D - 5) = 9(D - 5)

Now, we can solve for D, which represents the current age of Jeff's daughter. Expanding equation:

4D - 5 = 9D - 45

Next, move the variables to one side and the constants to the other side of the equation:

4D - 9D = -45 + 5

Combine like terms:

-5D = -40

Finally, solve for D:

D = -40 / -5

D = 8

Therefore, the current age of Jeff's daughter is 8 years old.

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