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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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