still confused..?

Question

At Mathesons family reunion there are three generations of family members, whose names are Betty, Georgia and two twins named John and Ian. If Georgia is 2 years and nine months older than Betty and the two twins are twice as old as Georgia, how old are Betty, Georgia, John and Ian if their ages total 217 years and three months?

Answer 1

Let J be the age of John and Ian(in months). Let G be the age of Georgia, and B the age of Betty (also in months).

We have:
G=B+33 (G=B+2*12+9)
J=G*2
B+G+2*J=2607 (B+G+J+J=217*12+3)

Now let's change J with G*2, because it is the same
we will have
G=B+33
B+5*G=2607
Now let's change G with B+33, because it is the same:
B+5*(B+33)=2607
6*B=2442
so B=407
G=440
J=880
To get their age in years divide those with 12
Betty's age is 33 (and 11 months)
Georgia's age is 36 (and 8 months)
And John and Ian each have 73 years and 4 months

Answer 2

let betty's age be x
then georgias's age = x+ 11/4(9 months = 3/4 years)
then age of 2 twins = 2(x+11/4) = 2x+11/2
total age
= x+ x+ 11/4 + 2(2x+11/2) ( twins = 2 persons same age)
= 6x+ 11 + 11/4 = 217 and 1/4
or 6x = 217 and 1/4 - 13 and 3/4 = 203 and 1/2 = 203 years and 6 monts
now this can be computed x = 33 years and 11 month
Betty 33 years 11 month
Georgia 36 years 8 months
John and Ian = 73 years 4 monnths

Answer 3

Lets start by making a variable for each person. Betty will be b, Georgia will be g and the twins will be t (remember they are both the same age)

So now we can write the equations from the words.

Convert 2 years and 9 months to 2-2/3 years so
g = 2-2/3 b
t = 2 g
b + g + t + t = 217-1/3

Now solve these three equations for the answer. You can do it!

Answer 4

Let x = age of Betty

Given:

Age of Georgia =x+2.75

Age of twin John = (x+2.75)2

Age of twin Ian = (x+2.75)2

Total age of Betty, Georgia, and twins =217.25

Adding all their ages, we get:

x+(x+2.75)+(x+2.75)2+(x+2.75)2=217.25

x+x+2.75+2x+5.5+2x+5.5=217.25

6x+13.75=217.25
6x=217.25-13.75
6x=203.50

Divide each side of the equation by 6:

x=203.5/6
x=33.92 years

Age of Betty = 33.92 years
Age of Georgia =33.92+2.75
=36.67years
Age of Twin John =36.67(2)
=73.34years
Age of Twin Ian =73.34years

Check: 33.92+36.67+73.34+73.34=217.27 (the difference of .02 is due to rounding off of numbers, but this is acceptable. So the answers must be correct. But I know why you are confused. Why three generations? I don't know. But never mind, you are not asked to answer that question anyway.
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