SOLUTION: Hi The sum of jans and bobs age is 18 years. When Jan is 3 years older than twice her present age, she will be 1.5 times as old as Bob will be in a year after that. How old

Question 1163215: Hi
The sum of jans and bobs age is 18 years. When Jan is 3 years older than twice her present age, she will be 1.5 times as old as Bob will be in a year after that.
How old is each one now.

Thanks

Found 3 solutions by Edwin McCravy, AnlytcPhil, Theo:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

Answer by AnlytcPhil(1807)   (Show Source): You can put this solution on YOUR website!
The sum of Jan's and Bob's age is 18 years.

J+B = 18

When Jan is 3 years older than
twice her present age,

That will be in k years, so J+k = 2J+3 Bob will then be B+k.

She (Jan) will be 1.5 times as old as Bob will be in a year
after that.

J+k = 1.5(B+k+1) B=3, J=15, k=18 Edwin

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
a = jan's age now.
b = bob's age now.
the sum of jan's and bob's age is 18.
a + b = 18
when jan is 3 years older than twice her current age, she will be 1.5 times as old as bob will be in a year after that.
when jan is 3 years older than twice her current age, jan will be 2a + 3 years old.
take 2a + 3 and subtract a from it to get a + 3.
jan will be 2a + 3 years old in a + 3 years.
bob will be b + a + 3 years old in a + 3 years.
bob will be b + a + 4 years old in a year after that.
therefore:
2a + 3 = 1.5 * (b + a + 4)
simplify to get:
2a + 3 = 1.5b + 1.5a + 6
subtract 1.5a from both sides of the equation to get:
.5a + 3 = 1.5b + 6
subtract 3 from both sides of the equation to get:
.5a = 1.5b + 3
divide both sides of the equation by .5 to get:
a = 3b + 6
since a + b = 18, replace a with 3b + 6 to get:
3b + 6 + b = 18
subtract 6 from both sides of the equation to get:
3b + b = 18 - 6
combine like terms to get:
4b = 12
solve for b to get:
b = 3
since a + b = 18, then you get:
a = 15
b = 3
the sum of their current ages is 18, which is correct.
2a + 3 = 33
1.5 * (b + a + 4) = 1.5 * (3 + 15 + 4) = 1.5 * 22) = 33.
2a + 3 = 1.5 * (b + a + 4) is correct.
the solution is confirmed to be good.
jan is now 15 years old
bob is now 3 years old
when jan is 2 * 15 + 3 years old, she will be 33 years old.
that will be 33 - 15 = 18 years from now.
18 years from now, bob will be 3 + 18 = 21 years old
1 year after that, bob will be 22 years old.
1.5 * 22 = 33
solution looks good based on my understanding of the problem.
based on that understanding, the solution is that jan is 15 years old now and bob is 3 years old now.

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