Question 1173699: In 5 years Kurt will be as twice as old as Vince. Five years ago, Kurt was three times as old as Vince. How old is each person now. Found 2 solutions by ewatrrr, mila nedic:Answer by ewatrrr(24785) (Show Source):
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.
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.
