A town's oldest inhabitant is x years older than the sum of the ages

Question

A town's oldest inhabitant is x years older than the sum of the ages of the Lee triplets. If the oldest inhabitants is now J years old, how old will one of the triplets be in 20 years?

A.  \frac{J - 50}{3}

B.  \frac{3(J + 20)}{x}

C.  \frac{J + x - 50}{3}

D.  \frac{J - x + 60}{3}

E.  \frac{J + x - 20}{3}

The answers is  (J-X+60)/3 .... But i was trying to solve it using algebra and got a wrong solution. I get this answer if i plug in numbers but i am trying to find the algebraic solution.

(J-X-40)/3 is my answers.

J = X + L + L + L is the initial situation
After 20 years
J + 20 = X + L + L + L + 60 ...(20 years for each triplet so 60 years totally).
(J - X - 40 ) / 3 = L is my answer.

What wrong am i doing ? Since the age asked is after 20 years i also consider adding 20 years to J .

Regards,
Mustu

sudhir18n · Answer

here it goes:

Oldest inhabitant = sum of age of triplets + X 
J = 3L + X so L = (J - X)/3

After 20 years = L + 20

= (J - X)/3 + 20

= (J - X + 60)/3

hope this helps

vinayrsm · Answer

hi mustu,

the initial eq is J=X+3L, your later equation i.e after 20 yrs J+20 = X+3L +60 is wrong as this is not what is stated. the relationship between J and L is only valid now and not after 20 yrs. therefore, you need to extract L from the initial eq and add 20 to it.

or you can do it as : J=X+Sum of triplets => sum of triplets = (J-X) and after 20 years: sum of triplets = J-X+60 => age of one triplet =(J-X+60)/3

Spidy001 · Answer

Current In 20 yrs

Oldest Inhabitant J = 3L +X 3L+X+20

Lee Triplet 1 L L+20

Lee Triplet 2 L L+20

Lee Triplet 3 L L+20

we are asked to find out triplets age in 20 yrs from now = L+20

from current we have J = 3L+X = > L = (J-X)/3

=> L+20 = (J-X)/3 +20 = (J-X+60)/3

Bunuel · Answer

Check other  Age Problems HERE .

gracie · Answer

t=age of one triplet
3t=J-x
t=(J-x)/3
t+20=(J-x)/3+20
t+20=(J-x+60)/3

testcracker · Answer

A town's oldest inhabitant is x years older than the sum of the ages of the Lee triplets. If the oldest inhabitants is now J years old, how old will one of the triplets be in 20 years? A. (J - 50)/3 B. 3(J + 20)/x C. (J + x - 50)/3 D. (J - x + 60)/3 E. (J + x - 20)/3 think simply J - 3L = x or L = (J - x)/3 in 20 years age of each "L" will be (J - x)/3 + 20 which implies (J - x + 60)/3 thanks

santisd1 · Answer

Hi, after reading all these I see the logic in keeping the "sum of the triplets" in mind..... but isn't that already accounted for in the original J = x+3L formula? As long as you're adding 20 to each side, aren't you already counting for each of the 3 "L"s? (ie --- J+20 = x+3(L+20) )

I'm running into the same problem as the OP and these explanations only half a little sense - I know 20x3 = 60... that's literally the only sensical party I understand from the jump of if L = (J -x)/3 , then in 20 years, that will be J-x + 60/3.... Especially since that 3 there SHOULD be counting (at least in my mind) for all the triplets....

Can someone break this down to an elementary level of how 20 years later becomes +60 in the equation?

My final formula was L+20 = ((J+20)-x)/3 
leading to... L = (J-40-x)/3

Thank you in advance!

amanvermagmat · Answer

Hi

First of all you need to be clear what is the meaning of 'L' in your solution. Are you taking L to be age of each triplet? OR are you taking L to be the 'sum of ages of 3 triplets'?

So lets say we take L to mean age of each of Lee's triplets. Then sum of their ages right now = L + L + L = 3L. So now we have J = x + 3L or 3L = J - x or L = (J - x)/3

Or we can say that age of each triplet right now = (J - x)/3. 
This means age of each triplet after 20 years = (J - x)/3 + 20 
Now this (J-x)/3 + 20 can also be written as: (J-x)/3 + 60/3 (since 20 = 60/3)
So this becomes = (J - x + 60) / 3

UserMaple5 · Answer

I was getting tripped up on the equation so decided to pick numbers:

Today:
Let J = 10
Let x = 1
Let EACH triplet be aged 3

So that gives us today: J = x + sum of the triplets
So today: 10 = 1 + (3+3+3)

In 20 years:

J = 10 +20 = 30
x = will be unchanged because it's a constant as per the question stem 
EACH triplet will be: 3 + 20 = 23 years old. The trap here is assuming that triplets will be 9 (I.e. the sum of their ages) + 20. This is not right.

Since each triplet is now 23 years old, the sum of their ages = 23 + 23 + 23 = 69.

So each triplet will be aged 69/3 = 23.

Just plug in your assumptions for J (=10) ; x (=1) and see which answer choice gives you 69/3. Answer D is the only one that fits

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A town's oldest inhabitant is x years older than the sum of the ages

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