Question

Two years ago a father was four times as old as his son. Three years from now the father will be only three times as old as the son. How old is each now?

If x represents the son's age two years ago, which expression represents his father's age three years from now?
1. x + 3
2. 3x + 3
3. 3x + 15

Answer 1

The answer is 2. 3x+3 :)

Answer 2

A)Let the present age of son be x

Present age of father be y

Ages 2 years ago

Son's age = x-2

Father's age = y-2

Two years ago a father was four times as old as his son.

So,
`y-2=4(x-2)` -- A

Three years from now

Son's age = x+3

Father's age = y+3

Three years from now the father will be only three times as old as the son.

`y+3=3(x+3)` ---B

Solve A and B

Substitute the value of y from A in B

`4(x-2)+2+3=3(x+3)`

`4x-8+2+3=3x+9`

`4x-3=3x+9`

`x=12`

So, son's present age = 12 years

father's present age =
`y-2=4(x-2)= y = 4(12-2)+2= 42`

So, father's present age is 42 years .

B) If x represents the son's age two years ago, which expression represents his father's age three years from now?

Two years ago son's age = x

Present age of son = x+2

Son's age after three years = x+2+3=x+5

Three years from now the father will be only three times as old as the son

Father's age after 3 years = 3(x+5)=3x+15

So, Option 3 is true