age problem algebra

Question

Kevin is 3 times as old as Daniel. 4 years ago, Kevin was 5 times as old as Daniel.

Answer 1

ax=B

therefore, ax+bx=c, x is the variable.

Kevin is 3 times as old as Daniel so K=3D, K being Kevins age and D being Daniels. (EQ.1)

4 years ago, Kevin was 5 times Daniels age meaning:

K-4=5(D-4)

distributing the 5 we get

K-4=5D-20D; leaving us with K=5D-16 when we combine like terms. (EQ. 2)

Using the substitution method and plugging in (EQ. 1) into (EQ. 2) we get the following:

3D=5D-16

-2D=-16, dividing by negative 1 we get

2D=16 leaving us with Daniels age (D) being 8. for EQ. 2

plugging in to EQ. 1 we get

K=3D giving us K=3(8) which makes Kevin's age 24.

Answer 2

Let Kevin's age be K

Let Daniel's age be D

Kevin is 3 times as old as Daniel = 3 times Daniel's age will be Kevin's age

K = 3D

Four Years Ago, Kevin was 5 times as old as Daniel

Since it is 4 years ago, we directly manipulate both ages D and K by 4 as such:

(K - 4)

(D - 4)

*We subtract 4 to represent "4 years ago".

Now, we apply the relationship that Kevin is 5 times as old as Daniel, meaning 5 times Daniel's age will be Kevin's age.

K - 4 = 5(D - 4)

Simplifying, we have: (Make sure to apply distributive property correctly when evaluating 5(D - 4))

K - 4 = 5D - 20

K = 5D - 16

Now we have a system of equations:

K = 5D - 16

K = 3D

Substituting K from the first equation into the second, we have:

5D - 16 = 3D

Simplifying

2D = 16

D = 8

Plugging this back into the second equation, we have

K = 3(8)

K = 24

Thus, Kevin is 24 years old and Daniel is 8 years old.

Currently Kevin is 3 times older than Daniel.

4 years ago, Kevin was 20 years old and Daniel was 4 years old.

At that time Kevin was 5 times older than Daniel.

Answer 3

Let Kevin's age be K

Let Daniel's age be D

Kevin is 3 times as old as Daniel = 3 times Daniel's age will be Kevin's age

K = 3D

Four Years Ago, Kevin was 5 times as old as Daniel

Since it is 4 years ago, we directly manipulate both ages D and K by 4 as such:

(K - 4)

(D - 4)

*We subtract 4 to represent "4 years ago".

Now, we apply the relationship that Kevin is 5 times as old as Daniel, meaning 5 times Daniel's age will be Kevin's age.

K - 4 = 5(D - 4)

Simplifying, we have: (Make sure to apply distributive property correctly when evaluating 5(D - 4))

K - 4 = 5D - 20

K = 5D - 16

Now we have a system of equations:

K = 5D - 16

K = 3D

Substituting K from the first equation into the second, we have:

5D - 16 = 3D

Simplifying

2D = 16

D = 8

Plugging this back into the second equation, we have

K = 3(8)

K = 24

Thus, Kevin is 24 years old and Daniel is 8 years old.

Currently Kevin is 3 times older than Daniel.

4 years ago, Kevin was 20 years old and Daniel was 4 years old.

At that time Kevin was 5 times older than Daniel.