Answer:
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, [tex]y-2=4(x-2)[/tex] -- 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.
[tex]y+3=3(x+3)[/tex] ---B
Solve A and B
Substitute the value of y from A in B
[tex]4(x-2)+2+3=3(x+3)[/tex]
[tex]4x-8+2+3=3x+9[/tex]
[tex]4x-3=3x+9[/tex]
[tex]x=12[/tex]
So, son's present age = 12 years
father's present age = [tex]y-2=4(x-2)= y = 4(12-2)+2= 42[/tex]
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
