Hi,

Previously posted

Using x for Vince's age NOW and y for Kurt's age NOW.

Write as You Read:

 y + 5 = 2(x+5)            * Used below to find y

 y - 5 = 3(x-5)            * Used below to check our work

Expand

 y + 5 = 2x + 10

 y - 5 = 3x - 15

Set Up

  y - 2x = 5

  y - 3x = -10 

Multiplying 2nd EQ by -1 to eliminate y

   x = 15 , Vince's age now  and Kurt is 35 

Checking our Work

 y - 5 = 3(x-5)

 30 = 30  checks

Wish You the Best in your Studies.  

Answer by mila nedic(19)   (Show Source): You can put this solution on YOUR website!
 Let's say Kurt's age is k and Vince's age is v. We can use these variables to create equations to help us solve the problem.

We have two pieces of information. In 5 years Kurt will be twice as only as Vince:(k+5)=2(v+5) and 5 years ago, Kurt was three times as old as Vince: (k-5)=3(v-5)



(k+5)=2(v+5)

k+5=2v+10

k-2v=5

k=5+2v (now that we have solved for k we can use it for the next equation so we are only dealing with one variable at a time.



(k-5)=3(v-5)

k-5=3v-15

k-3v=-10 (simplify this equation as much as possible)

(5+2v)-3v=-10 (input 5+2v instead of k so we can solve for v)

5-v=-10

-v=-15

v=15 (Vince is 15 years old)



Now we can use one of the first equations to solve for Kurt's age. Let's take (k+5)=2(v+5)

k+5=2(15+5) (we replace v with 15 because we know that v=15)

k+5=40

k=35 (Kurt is 35 years old)



To check our work we can use the second equation to see if we are correct.

(k-5)=3(v-5)

35-5=3(15-5) (we replace k with 35 and v with 15)

30=30 (since they are equal we know our answers are correct)



Therefore Vince is 15 years old and Kurt is 35 years old. 

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