SOLUTION: Bill is 5 times older than Keira, Bill is 5 times older than Phil, Oscar is twice as old as Bill, and the total age of all of them at 81. How old is Phil?

Question 1183664: Bill is 5 times older than Keira, Bill is 5 times older than Phil, Oscar is twice as old as Bill,
and the total age of all of them at 81. How old is Phil?
Found 4 solutions by ikleyn, greenestamps, ankor@dixie-net.com, josgarithmetic:
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.
Bill is 5 times older than Keira, Bill is 5 times older than Phil, Oscar is twice as old as Bill,
and the total age of all of them at 81. How old is Phil?
~~~~~~~~~~~~~~~~~~~

In English, the forms like this   "Bill is 5 times older than Keira"   are prohibited in Math problems formulations.

In this part, English is very different from many other languages.

            (In this part, English is RADICALLY different from many other languages,
            and the newcomers, as a rule, don't know and even don't suspect about it ( ! ) )

Therefore, when you translate from your native language, be careful -- you should know standard English patterns
for the subject to which you create/translate your problem.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

ANSWER: NO SOLUTION!

The statement of the problem is faulty. Age problems need to have answers that are whole numbers; this one does not -- regardless of how it is interpreted.

The statement of a math problem should never say that one person is "5 times OLDER THAN" another person.

In sloppy everyday English usage, "5 times OLDER THAN" and "5 times AS OLD AS" are used to mean the same thing, but they do not. If the first person's age is x, then the age of a person 5 times AS OLD AS the first is clearly 5 times x, or 5x. But if the age of the second person is 5 times OLDER THAN the first, then that person's age is x, PLUS 5 MORE TIMES x, which is x+5x=6x.

This problem is faulty in that the answers are not whole numbers with either interpretation of the given information.

(1) If we incorrectly use 5 times older than x to mean 5x, then
Phil = x
Bill = 5x
Keira = x
Oscar = 10x

The sum of their ages is 81:
17x=81
x = 81/17 not a whole number

(2) if we correctly use 5 times older than x to mean 6x, then
Phil = x
Bill = 6x
Keira = x
Oscar = 12x

20x=81
x = 81/20 not a whole number

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Bill is 5 times older than Keira,
b = 5k
Bill is 5 times older than Phil,
b = 5p
Oscar is twice as old as Bill,
o = 2b
and the total age of all of them at 81.
b + k + p + o = 81
Something wrong here, as written, this will not produce an integer solution which is generally required in problems like this.
Change a couple words in this problem, it works then
"
Bill is "3 years" older than Keira,
b = k + 3
k = b - 3
Bill is 5 times older than Phil,
b = 5p
divide both sides by 5
p = .2b
Oscar is twice as old as Bill,
o = 2b
and the total age of all of them at 81.
b + k + p + o = 81
replace: k with (b-3), replace p with .2b and o with 2b
b + (b-3) + .2b + 2b = 81
4.2b = 81 + 3
b = 84
b = 84/4.2
b = 20 yrs old is bill
then
k = 20-3 = 17 yrs is Keira
and
p = .2*20 = 4 yrs is Phil
and
o = 2 * 20 = 40 yrs is Oscar
:
Check: 20 + 17 + 4 + 40 = 81
:
Anyway this is the method.

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Strange description.
If "Bill is 5 times older than Keira, Bill is 5 times older than Phil,", then Keira and Phil are the same age.

Bill k+5k=p+5p Keira k Phil p Oscar 2(k+5k)=2(p+5p) TOTAL 81

That table can be simplified because the simple addition and k=p.

Bill 6p Keira p Phil p Oscar 12p TOTAL 81

Question asked essentially for p.
RELATED QUESTIONS
Jason is 5 years older than Bill. Bill is twice as old as Sharon. How old is... (answered by richwmiller)
Bill is twice as old as Joyce and Sam is five years older than Bill if Joyce is n years (answered by lwsshak3)
Fred is 25 years older then Bill. In 5 years times he will be twice as old as Bill find... (answered by Maths68)
jason is 5 years older then bill and bill is twice as old as sharon how old is... (answered by josmiceli)
Bill is ten years older than his brother, Alex. There was a time when Bill was three... (answered by math_helper)
john is twice as old as bill. greg is 7 years older than bill. four years ago, the sum of (answered by JBarnum)
Ann and Bill's age adds up to 91. Ann is now three times as old than what Bill was when... (answered by ankor@dixie-net.com)
how old is each person. If jose is five years older than amanda.Mike is twice as old as... (answered by ankor@dixie-net.com)
Bill is 2 years older than his brother and 5 years younger than his sister. 5 years ago... (answered by ankor@dixie-net.com)