a mathametical problem in 10 th class.(related to age of father,mother & son)?

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 5:4 and sum of ages of father, mother & son is 70.
find the ages of father, mother & son.

Answer 1

Let the ages be F, M and S in years (whole numebers)

Since Father's age is divisible by son's age, therefore

F = S X n1

Since Mohter's age is divisible by son's age, therefore

M = S X n2

where n1 and n2 are positive whole numbers



Ratio of Father and Mother's age is 5:4

=> F/M = 5/4

Substitue for F and M

(S X n1)/(S X n2) = 5/4

=> n1/n2 = 5/4

=> n1 = 5/4 X n2



Since the sum of their ages is 70, therefore

F + M + S = 70

=> S X n1 + S X n2 + S = 70

=> S X 5/4 X n2 + S X n2 + S = 70

=> S(5/4 n2 + n2 + 1) = 70

Multiply by four both sides of the equation



=> S (5 n2 + 4 n2 + 4) = 280

=> S (9 n2 + 4) = 280

Substute positive integers values to n2, compute the value of (9 n2 + 4) and verify wether it is a factor of 280?



n2 (9 n2 + 4) Factor of 280

1 13 No

2 22 No

3 31 No

4 40 Yes



Therefore, n2 = 4, n1 = 5/4 X 4 = 5: n1 = 5

F = n1 X S = 5 S

M = n2 X S = 4 S



Since

S (9 n2 + 4) = 280

S (36 + 4)= 280, therefore,

S = 280 / 40 = 7

F = 5 S = 5 X 7 = 35

M = 4 S = 4 X 7 = 28



Therefore their ages are

Father = 35 years

Mother = 28 years

Son = 7 years

Answer 2

Problem:

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 5:4 and sum of ages of father, mother & son is 70.

find the ages of father, mother & son.



Solution:

Let x be the age of the son

4x be the age of the mother

5x be the age of the father



x + 4x + 5x = 70 reason: given

10x = 70 reason: combine similar terms

x = 7 reason: Multiplicative Property of Equality



Ages: (reasons: Substitution)

Son = x = 7 years old

Mother = 4x = 28 years old

Father = 5x = 35 years old



Check:

The equation was x + 4x + 5x = 70, so if we use substitution, the equation will be 7 + 28 + 35 = 70, so if we combine similar terms, then the result would be 70 = 70..... There you go!

Answer 3

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Now the solution:

Let the ages be F, M and S in years (whole numebers)

Since Father's age is divisible by son's age, therefore

F = S X n1

Since Mohter's age is divisible by son's age, therefore

M = S X n2

where n1 and n2 are positive whole numbers



Ratio of Father and Mother's age is 5:4

=> F/M = 5/4

Substitue for F and M

(S X n1)/(S X n2) = 5/4

=> n1/n2 = 5/4

=> n1 = 5/4 X n2



Since the sum of their ages is 70, therefore

F + M + S = 70

=> S X n1 + S X n2 + S = 70

=> S X 5/4 X n2 + S X n2 + S = 70

=> S(5/4 n2 + n2 + 1) = 70

Multiply by four both sides of the equation



=> S (5 n2 + 4 n2 + 4) = 280

=> S (9 n2 + 4) = 280

Substute positive integers values to n2, compute the value of (9 n2 + 4) and verify wether it is a factor of 280?



n2 (9 n2 + 4) Factor of 280

1 13 No

2 22 No

3 31 No

4 40 Yes



Therefore, n2 = 4, n1 = 5/4 X 4 = 5: n1 = 5

F = n1 X S = 5 S

M = n2 X S = 4 S



Since

S (9 n2 + 4) = 280

S (36 + 4)= 280, therefore,

S = 280 / 40 = 7

F = 5 S = 5 X 7 = 35

M = 4 S = 4 X 7 = 28



Therefore their ages are

Father = 35 years

Mother = 28 years

Son = 7 years



Good luck

Answer 4

Father 35 Mother 28 Son 7

Answer 5

ratio of father & mother is 5:4,

so, 5x ,4x

sum is 70,

x+5x+4x = 70.

10x = 70

x = 7.



son age = 7 yr.

Father age = 35 yr

Mother age = 28 yr.

(35 & 28 are devidable by 7)

Answer 6

Suppose the son's age is X. As mothers and Fathers age aare in multiples of Son's age and they are in the ratio 5:4,

their ages have to be 5X and 4X respectively



Then

X+5X+4X=70

= 10X =70

X=7

therefore's sons age 7 years, fathers age 35 and mother's age 28



Thats all

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Actually i have passed my X exams last year and secured 93% and so i am goodd at maths

Answer 7

father age 35 , mother 28, son 7

Answer 8

Father's age= 40; mothers age= 30; son=just born baby.

Answer 9

70 is multiple of 7

ratio of 5:4 means 35 and 28

sons age 70 minus 63 means7

7 is divisable to 35 n 28

hence ages are

father 35

mother 28

son 7

Answer 10

father age-35 years

mother age-28 years

son age-7 years

Answer 11

35 , 28 , 7 .

Answer 12

father: 35

mother: 28

son: 7



x + 4x + 5x = 70

10x = 70

Answer 13

damn. Ratios was one thing i was never good at

Answer 14

35,28,7