John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages will be 60 . How old is John

Question

Please show me complete solutions and answer. Thanks. John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages will be 60 . How old is John now?

Answer 1

So let F be the father, J be John, and A be Alice

We will create a system of equations:

 

(1)   F=5J

(2)   J=2A

(3)   (F+2)+(J+2)+(A+2)=60

 Let's simplify this last one:  F+J+A+6=60  ->  F+J+A=54

 

Now we can substitute. Let's start by putting (1) into (3) to form eq (4):

5J+J+A=54

 

Now we can substitute information from equation (2) into equation (4):

5(2A)+2A+A=54

10A+2A+A=54

13A=54

A=54/13

A=4.15

 

J=2A

J=2(54/13)

J=108/13

J=8.31

 

F=5J

F=5(108/13)

F=540/13

F=41.54