In 2 years Peter will be twice as old as his sister Eve. The sum of their presents ages is 26. Find their ages.

Question

Word problems

Answer 1

Hi Ally,

 

Let's begin by assigning variables (letters) for our two unknowns:

    P = Peter's age

     E = Eve's age

 

Now let's come up with two equations we can use to solve for our two unknowns from the given information in our problem:

 

First, we are told that in 2 years Peter will be twice as old as Eve.  We can represent this fact by our first equation (Equation #1):

 

Equation #1:  P + 2 = 2(E + 2)

 

Next, we are told that the sum of their ages now is 26.  We can represent this fact by our second equation (Equation #2):

 

Equation #2:  P + E = 26

 

Let's rewrite Equation #1 in the format of Equation #2 (all variables on the left side and constant on the right side):

 

P + 2 = 2(E + 2)
P + 2 = 2E + 4 (distribute 2 on right side)
P - 2E = 2 (move and combine like terms)

 

Now let's look at both equations and see if by combining them we can eliminate one of the variables:

 

Equation #1:  P - 2E = 2

Equation #2:  P + E = 26

 

We can eliminate the variable P by subtracting Equation #2 from Equation #1 to get Equation #3:

 

Equation #3:  -3E = -24

 

Now we can solve for variable E (Eve's age) using Equation #3:

    -3E = -24

     3E = 24 (multiply both sides by negative 1)

       E = 8 (divide both sides by 3)

 

So now we know that Eve's age is 8. 

 

Now we can plug in the value for Eve's age into Equation #2 and solve for P (Peter's age):

  P + E = 26    

  P + 8 = 26 (plug in)

  P = 18 (subtract 8 from both sides)

 

So now we know that Peter's age is 18.

 

We can check to see if our answers are correct by plugging in the values for both ages into Equation #1:

    P + 2 = 2(E + 2)          

    18 + 2 = 2(8 + 2) ... plug in   

          20 = 2(10) ....... addition on both sides

          20 = 20 ........... multiplication on right side

         

Both sides of the equation match, so we know that our answers are correct.

 

Thanks for submitting this problem and glad to have been of help.

 

Regards, Jordan.

Answer 2

This requires a system of two equations.

 

peters age = x

eve's age = y

 

the equation for their current ages is x + y = 26

now, in two years eve will be y +2 years old. Peter will be twice as old as Eve then so Peter will be 2(y+2) years old. Therefore, the second equation is

x +2=2(y+2).  We must add 2 to the right side to account for Peter being two years older.

 

solve the system: x + y = 26

                           X +2= 2(y+2) or x = 2y +2 after we solve for x. 

substitution seems to be the easiest solution method. Plug the simplified bottom equation into the top and get:

 

2y+2+y = 26

3y +2=26

3y=24

y =8. And x = 2(8)+ 2 = 18

 

peter is 18 and Eve is 8 years old.

in two years Peter will be 20 and Eve will be 10.

 

i hope this helps you!

Answer 3

p=Peter's age

e=Eve's age

p+e=26

p+2=2(e+2)

from p+e=26 we get p=26-e

substitute

26-e+2=2(e+2)

28-e=2e+4

28-4=2e+e

24=3e

e=8 years old

p=26-8=18 years old