3years ago a father was 3 times as old as his son, in five years time he will be twice as old as his son, what will be the sum of their years in four years time

46 years

Step-by-step explanation:

Let the father's age be x and the son's age be y, then 3 years ago:

Father = x - 3

son     = y - 3

Then , from the first statement :

x - 3 = 3 ( y - 3 )

x - 3 = 3y - 9

x     = 3y - 9 + 3

x     = 3y - 6 equation 1

In five years time

father = x + 5

son = y + 5

Then , from the second statement

x + 5 = 2 ( y + 5 )

x + 5 = 2y + 10

x       = 2y + 10 - 5

x       = 2y + 5 equation 2

Equating equation 1 and 2 , we have

3y -6 = 2y + 5

add 6 to both sides

3y = 2y + 5 + 6

subtract 2y from both sides

3y - 2y = 11

y = 11

substitute y = 11 into equation 1 to find the value of x

x = 3y - 6

x = 3(11) - 6

x = 33 - 6

x = 27

This means that the father is presently 27 years and the son is presently 11 years.

In four years time

father = 27 + 4 = 31

son = 11 + 4      = 15

sum of their ages in four years time will be

31 + 15 = 46 years

46 years

Step-by-step explanation:

Step-by-step explanation:

In solving this, we'll make some keen assumptions to solve the question.

We'll represent the father's age with "a"

And represent the sons age as "b"

Lets interpret the question.

3 years ago, (means in the past), we'll subtract.

Therefore:

Father's age = a - 3

Sons age = b - 3

The sentence said, " 3 years ago, father was 3 times the sons age*. Interpreting that becomes:

a - 3 = 3 times (b - 3)

Simplifying that gives :

a - 3 = 3(b - 3)

a - 3 = 3b - 9

a = 3b - 9 + 3

a = 3b - 6 ( FIRST EXPRESSION )

The next line says: In five years time (that's in the future, hence we add) he'll be twice his sons age.

Therefore I become:

Father : a + 5

Son : b + 5

a + 5 = 2(b + 5)

a + 5 = 2b + 10

a = 2b + 5 ( SECOND EXPRESSION)

Equating the first and second equation to solve for "a" - the father's age

3b - 6 = 2b + 5

b = 5 + 6

b = 11 years (Sons age)

Substitute b = 1 in the first expression.

a = 3b - 6

a = 3(11) - 6

a = 33 - 6

a = 27 years (Father's age)

Let resolve, the last sentence:

What will be the sum of their ages in 4 years time. (SINCE IT'S IJ THE FUTURE, WE ADD)

Father's age in four years time: 27 + 4 = 31

Son's age in four years time: 11 + 4 = 15.

The sum of their ages in same four years time becomes:

31 + 15 (years)

46 years

i got 86 for this

hope this !

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