How Old Are Andy and Cal in This Mathematical Age Puzzle?

[K Sengupta]

Two friends Andy and Cal form a team together. Andy is as old as Cal will be when Andy is twice as old as Cal was when Andy was half as old as the sum of their current ages. Cal is as old as Andy was when Cal was half as old as he will become in ten years.

Determine the respective current ages of Andy and Cal from the abovementioned statements.

 

[ƒ(x)]

Assuming that 0 and 0 are not acceptable answers
Oh, didn't read that last sentence.

 

[ƒ(x)]

Spoiler

Same age
ehh nevermind :( umm cal is 8 and Andy is 6?

Work will follow later, its bedtime now.

 

[Borek]

In a way similar to the question I have posted here: https://www.physicsforums.com/showthread.php?t=245602

 

[ƒ(x)]

Borek, this problem does seem more complicated that yours though.

 

[Borek]

Yes, in my problem total is given.

 

[ƒ(x)]

umm...does this even have a solution? The sentences contradict one another in regards to the verb tenses.

 

[regor60]

Spoiler

Andy is 40, Cal 30
Last sentence first. "was"=x, "will be"=y incremental years, respectively.
C=A-X; C-X=1/2(C+10) so X=1/2C-5 therefore C=A-1/2C+5 so 3/2C-A=5 (1)
First sentence.
A=C+Y;A+Y=2(C-X) > different X than above, just an intermediate
A-X=(A+C)/2; X=A/2-C/2. Sub into above
A+Y=2(C-A/2+C/2); Y=3C-2A
A=C+3C-2A;4C=3A;C=(3/4)A (2);
sub (2) into (1)
(9/8)A-A=5>>>>>A=40
From (2) C=30
Check:
Last sentence:
Cal is as old as Andy was > Cal is 30 and Andy was 30 10 yrs ago. 10 yrs ago Cal was 20. Is this half as old as Cal will be in 10 yrs ? Cal now 30+10 divide by 2 = 20 >>check
First sentence:
Half sum of current ages =35. Andy now 40 so this is 5 yrs ago. Cal was 25 then. Andy will be twice as old as this = 50 = 10 yrs from now. Is Andy now as old as Cal will be 10 yrs from now ? Cal is 30 +10 = 40 =Andy's age now>>check

I'd like that hour of my life back thank you

 

[ƒ(x)]

Spoiler

Andy is 40, Cal 30
Last sentence first. "was"=x, "will be"=y incremental years, respectively.
C=A-X; C-X=1/2(C+10) so X=1/2C-5 therefore C=A-1/2C+5 so 3/2C-A=5 (1)

I'd like that hour of my life back thank you

Why did you do C = A - X? When I tried this I used compound functions--C(x) = x and A(x) = x + a--why didnt that method work?

 

[regor60]

Why did you do C = A - X? When I tried this I used compound functions--C(x) = x and A(x) = x + a--why didnt that method work?

C=A-X just reflects the statement that "Cal is as old as Andy was..." meaning Cal's age now, C, is the same as Andy's was, meaning some years, X, before Andy's current age, A.

Further, C-X is just Cal's age X years ago, referenced to his age, C, now

I don't know what a compound function is so can't help there