Question

Jack is 27 years older than Susan. In 5 years he will be 4 times as old as she is. Find the present ages of jack and Susan

Answer 1

x - Jack's age
y - Susan's age

Jack is 27 years older than Susan.

`x=y+27`

In 5 years he will be 4 times as old as she is.

`x+5=4(y+5)`

The system of equations:

`x=y+27 \\ x+5=4(y+5) \\ \\ \hbox{substitute y+27 for x in the 2nd equation:} \\ y+27+5=4(y+5) \\ y+32=4y+20 \\ y-4y=20-32 \\ -3y=-12 \\ y=(-12)/(-3) \\ y=4 \\ \\ x=y+27=4+27=31`

Jack is 31 years old and Susan is 4 years old.