First right answer with proper explaination of the mathametical problem get 10 points.?

Question

the ages of father, mother & son are in round figure. both father & mother ages are devidable by the son's age.the ratio of father & mother age is 4:3 and sum of ages of father, mother & son is 60.
find the ages of father, mother & son. (the age of son< 7 years)

Answer 1

let son's age : S
mother's age: M
fathers age: F
Given F/M = 4/3 or F = (4/3)M
Also S + M + F = 60
or, S + M + (4/3)M = 60
or, S + (7/3) M = 60 ............ (1)
Now, its given that M is multiple of S
so, S + (7/3) S.k = 60 (where k is a positive integer)
or, S(1 + 7k/3) = 60
or, S (3 + 7k) = 180
Now 180 = 2 x 2 x 3 x 3 x 5
since S < 7given, S could be 2 , 3 , 4, or 5.
and (3+7k) would be 90, 60, 45 or 36. Since k is an integer (3+7k) will take the value 45 for k = 6. There does not exist any integer k for which (3+7k) = 90 or 60 or 36.
hence S = 4.
and M = (60 - 4) x (3/7) = 24..... from equation(1)
and F = (4/3) M = (4/3) x 24 = 32

Finally Son's age = 4, Mother's age = 24 and Father's age = 32

Answer 2

Answer: (with proper procedure.)
let son's age : S
mother's age: M
fathers age: F
Given F/M = 4/3 or F = (4/3)M
Also S + M + F = 60
or, S + M + (4/3)M = 60
or, S + (7/3) M = 60 ............ (1)
Now, its given that M is multiple of S
so, S + (7/3) S.k = 60 (where k is a positive integer)
or, S(1 + 7k/3) = 60
or, S (3 + 7k) = 180
Now 180 = 2 x 2 x 3 x 3 x 5
since S < 7given, S could be 2 , 3 , 4, or 5.
and (3+7k) would be 90, 60, 45 or 36. Since k is an integer (3+7k) will take the value 45 for k = 6. There does not exist any integer k for which (3+7k) = 90 or 60 or 36.
hence S = 4.
and M = (60 - 4) x (3/7) = 24..... from equation(1)
and F = (4/3) M = (4/3) x 24 = 32

Finally Son's age = 4, Mother's age = 24 and Father's age = 32

Answer 3

given ages of father, mother and child are round figures.
let us suppose the age of son is x
since it was given ages of father and mother are divisible by the age of son and also in the ratio 4:3, the ages of father and mother can be taken as 4kx and 3kx (where k is an integer)without loss of generality. And also given total of all of them is 60. which means 4kx+3kx+x= 60 or 7kx+x=60 and x is an integer. for x and k to be integers, the only possible values are, x=4 and k=2. For x less than 4, k will be an improper fraction anf for x=5, 6 it will be a proper fraction. hence the ages of father , amother and son are respectively, 32, 24, and 4.

Answer 4

dipid's reasoning is almost, but not quite correct.

The son is 4; the mother is 24 and the father is 32

Proper explanation:

Let x = the son's age
let mx = mom's age
and fx = father's age

we are given: fx/mx = f/m = 4/3 so f = 4m/3
we are also given:
x+mx+fx = 60
x(1+m+f) = 60
x(1+m+4m/3) = 60
x(3+7m)/3 = 60
(1)......x(3+7m) = 180
We are given x < 7 and also all the ages are integers.
But since 1,2,3,4,5, and 6 all divide 180, without further examination x could any of these six numbers.
However note that (1) implies 7 divides (180/x) -3; that is: 7 divides 180-3x. But also 7 divides 180-5 (=175)
Therefore 7 divides 180-5-(180-3x)= 3x-5
It is immediately obvious that x=4 since 3(4)-5=7
So m= ((180/4)-3)/7 = 6 and f = 4(6)/3 =8
So x = 6; mx =24 and fx = 32

Answer 5

Father : 34
Mother: 24
Son : 2

All ages in round figure. Father (34) and mothers age(24) is divisible by sons age (2). 34:24 = 4:3. Sum of 34, 24 and 2 = 60.
Son's age is less than 7 years.

Trial and error!!

Ten points to me???

Answer 6

Age of father = 32
Age of mother = 24
Age of Son = 4

Answer 7

father 28 mother 24 son 8

Answer 8

let son's age be x
fathers be 4y
moms be 3y
x+4y+3y=60
x+7y=60
son's age is less than 7. and all have round figures.

suppose x=6
then y=54/7. answer not round figure
suppose x=5 then y=55/7, wll not give dads n moms as round fig.
sppose x(son's)=4 then y=8 and the dad will be 32 mom 24 all three add upto 60. thats the ans.
another way to reach at the ans s to check the eq: x+7y=60.
y has to be a whole no. so x has to be 4 to give the nearest multiple for 7! i used trial and error as you can see.

Answer 9

let son age be 4
then the sum of both father and mother age will be 56
the ratio of father and mother is 4:3 (given)
therefore father age is 32 years
and mother age will be 24 Years
son age is 4 years

Answer 10

the parents are both 0 years old and the son is 60

reason :

in question given parents ages are ROUND figures hence=0

0:0 is undefined and hence can take any value

hence0:0=4:3

0 is divisable by any number and hence also by 60

the sum of the ages are 0+0+60=60

thus proved