age problem algebra

Question

Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel. how old is daniel now.

Answer 1

Hi Gin!

To solve this problem, we'll need to write some equations using variables to represent the boys' ages.

To keep it simple, let's use K for Kevin's age now and D for Daniel's age now.

Kevin is 3 years older than Daniel.

K = D + 3

Two years ago, Kevin was 4 times as old as Daniel.

For this part, you'll need to subtract 2 from BOTH boy's ages.

K - 2 = 4(D - 2)

How old is Daniel now?

Let's use substitution to find the value of D.

Since we know from the first part of the problem that K = D + 3, and we're trying to get D by itself, let's substitute D + 3 for the K in the second equation.

So now we'll have:

D + 3 - 2 = 4(D - 2)

D + 1 = 4(D - 2) Because 3 - 2 = 1

D + 1 = 4D - 8 Because you have to multiply both the D and the 2 by 4

Now, we want to get D by itself to find Daniel's current age. So we'll want to have all the D values on the left side of the equation. To get rid of the 4D on the right, we'll need to subtract 4D. And whatever we do to one side of an equation, we need to do to the other, so:

D + 1 - 4D = 4D - 4D - 8 Subtract 4D from each side.

-3D + 1 = -8 Because D - 4D = -3D, and 4D - 4D = 0.

-3D + 1 - 1 = -8 - 1 On the left, we want only the D values, so we subtract 1 from each side.

-3D = -9 Because 1 - 1 = 0, and -8 - 1 = -9.

-3D/-3 = -9/-3 To get D by itself, we divide both sides by - 3.

D = 3 -3D/-3 = D, and -9/-3 = 3.

Daniel is 3 years old.

I hope this helps!

Kelsey

Answer 2

Let K represent Kevin's age.

Let D represent Daniels age.

Kevin is 3 years older than Daniel. This can be expressed as:

K = 3 + D

Two years ago, Kevin's age was K-2 and Daniels age was D - 2. So we use these to write an expression for their ages 2 years ago.when Kevin was 4 times as old as Daniel:

K-2 = 4*(D-2)

Now we will will simplify the equation by distributing the 4

K-2 = 4D -8 Now we will replace K for D + 3

D + 3 -2 = 4D - 8 Combine all D's on the right side.

1 = 3D - 8 Add 8 to both sides.

9= 3D Divide by 3

3 = D

Daniel is 3 years old.

Now we check our answer. If Daniel is 3 than Kevin must be 6 years old. Two years ago, Daniel would be 1 and Kevin would be 4. So 2 years ago, Kevin would be four times as old as Daniel.

Answer 3

In solving mathematical word problems the number of unknowns is the number of equations that you will need to solve it. In our problem here our unknowns are Kevin's age and Daniel's age, which means we need 2 equations to solve it.

Let D= Daniel's age

K= Kevin's age

Equation 1 Equation 2

Kevin is 3 years older than Daniel : Two years ago Kevin was 4 times Daniel's age:

K=D+3 K-2=4(D-2)

We can solve this by using either the substitution or elimination method. Using the substitution method, we will use Eq. 1 for the value of K and put that into Eq. 2:

Eq. 1: K=D+3 Put this value of K into Eq. 2 and solve for D;

Eq. 2: K-2=4(D-2) ----> (D+3)-2=4(D-2) ----> D+1=4D-8 ---->8+1=4D-D ----> 9=3D ----> 3=D

Now we take this value of D and put it into either Eq. 1 or Eq. 2 to solve for K. Using Eq. 1 we get:

K=D+3 ----> K=3+3 ----> K=6

You will see that these values also work for Eq. 2, so you know that these are correct.

Therefore, the answer is that Daniel is 3 years old.

Hope this helps!

Answer 4

Let's start by defining variables.

K- Kevin's age now

D- Daniel's age now

Now, we brainstorm equations from the original information that connect these two variables.

D + 3 = K Kevin is three years older than Daniel. So, if you add 3 to Daniel's age, you get Kevin.

K - 2 = (D-2)*4 Two years ago (K - 2) Kevin was four times as old as Daniel (D - 2 because 2 years ago).

Now that we have two variables and two equations, we can use a systems of equations strategy to solve. I am going to choose to substitute one variable for the other, leaving me with one variable that I can solve for. I will explain each step in words to the right of the math.

K = D + 3

K - 2 = 4D - 8 These are the original equations after you expand the second one (multiply the 4 through).

D + 3 - 2 = 4D - 8 Substitute the first equation into the second. (Every K becomes D - 3).

D + 1 = 4D - 8 Solve the subtraction on the left side.

D + 9 = 4D Add 8 to both sides.

9 = 3D Subtract D from both sides to get the variables on one side and the numbers on the other.

3 = D Divide both sides by 3 to solve for D.

If D = 3 and D + 3 = K then 3 + 3 = 6. K = 6. To figure this out, I simply plugged in D = 3 into one of my original equations (D + 3 = K).

To answer the original question, Daniel is 3. Kevin is 6 (extra information).

Check Our Work:

Currently, Daniel is 3 and Kevin is 6. Based on the original information, they must be 3 years apart, which is true.

Now, it also must be true that 2 years ago Kevin was 4 times as old as Daniel. Two years ago, Daniel was 1 (3 - 2 = 1) and Kevin was 4 (6 - 2 = 4). Is Daniel's age (1) multiplied by 4 equal to Kevin's age (4)? Yes! So we are correct.

Answer 5

Let's start by defining variables.

K- Kevin's age now

D- Daniel's age now

Now, we brainstorm equations from the original information that connect these two variables.

D + 3 = K Kevin is three years older than Daniel. So, if you add 3 to Daniel's age, you get Kevin.

K - 2 = (D-2)*4 Two years ago (K - 2) Kevin was four times as old as Daniel (D - 2 because 2 years ago).

Now that we have two variables and two equations, we can use a systems of equations strategy to solve. I am going to choose to substitute one variable for the other, leaving me with one variable that I can solve for. I will explain each step in words to the right of the math.

K = D + 3

K - 2 = 4D - 8 These are the original equations after you expand the second one (multiply the 4 through).

D + 3 - 2 = 4D - 8 Substitute the first equation into the second. (Every K becomes D - 3).

D + 1 = 4D - 8 Solve the subtraction on the left side.

D + 9 = 4D Add 8 to both sides.

9 = 3D Subtract D from both sides to get the variables on one side and the numbers on the other.

3 = D Divide both sides by 3 to solve for D.

If D = 3 and D + 3 = K then 3 + 3 = 6. K = 6. To figure this out, I simply plugged in D = 3 into one of my original equations (D + 3 = K).

To answer the original question, Daniel is 3. Kevin is 6 (extra information).

Check Our Work:

Currently, Daniel is 3 and Kevin is 6. Based on the original information, they must be 3 years apart, which is true.

Now, it also must be true that 2 years ago Kevin was 4 times as old as Daniel. Two years ago, Daniel was 1 (3 - 2 = 1) and Kevin was 4 (6 - 2 = 4). Is Daniel's age (1) multiplied by 4 equal to Kevin's age (4)? Yes! So we are correct.

Answer 6

Daniel's age=x

Kevin's age=x+3

(x+3-2)=4(x-2)

x+1=4x-8

9=3x

x=3 years old, Daniel's age now