Word problem

Question

Two years ago, a father was five times as old as his son. Two years from now, his age will be 8 times more than three times the age of his son. Find the present age of father and son

Answer 1

f = father's current age

s = son's current age

 

(f-2) = 5(s-2)  equation 1

 

(f+2) = 8[3(s+2)]  equation 2

 

Rearrange equation 1:

(f-2) = 5(s-2)

f-2 = 5s - 10

5s - f = 8

 

 

Rearrange equation 2:

(f+2) = 8[3(s+2)]

f + 2 = 24(s+2)

f + 2 = 24s + 48

24s - f = -46

 

We have two simultaneous equations:

5s - f = 8

24s - f = -46

 

multiply 1st equation by -1 and add equations

-5s + f = -8

 24s - f = -46

19s = -46

s = -46/19

 

As you can see there is apparently a mistype in your problem

statement since the son's age will be a negative number.

 

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I think you meant to say:

Two years from now, his age will be 8 more than three times the age of his son.

 

f-2 = 5(s-2)

5s - f = 8     equation 1

 

(f+2) = 8 + 3(s+2)

f + 2 = 8 + 3s + 16

f + 2 = 3s + 24

3s - f = -22   equation 2

 

5s - f = 8     equation 1

3s - f = -22   equation 2

 

multiply equation 2 by -1 and add equations

 

5s - f = 8

-3s+f = 22

-----------------

2s = 30

s = 15

 

Son is 15 years old

 

substituting into equation 1:

5s - f = 8 

5(15) - f = 8

75 - f = 8

-f = -67

f = 67

 

father is 67 years old