Question

A father is three times as old as his son . After fifteen years the father will be twice as old as his son's age at that time. Hence what will be the fathers present age ?

Answer 1

Let's solve this problem step-by-step.

STEP-BY-STEP EXPLANATION:

We will be using simultaneous equations to solve this problem.

Let's establish the two equations we will be using to solve the problem.

Let present age of father = f

Let present age of son = s

Equation No. 1 -

f = 3s

Equation No. 2 -

f + 15 = 2s

To begin with, we will substitute the value of ( f ) from the first equation into the second equation to solve for ( s ).

Equation No. 2 -

f + 15 = 2s

( 3s ) + 15 = 2s

3s - 2s = - 15

s = - 15

Next we will substitute the value of ( s ) from the second equation into the first equation to solve for ( f ).

Equation No. 1 -

f = 3s

f = 3 ( - 15 )

f = - 45

FINAL ANSWER:

Therefore, the present age of the father is - 45 years old.

It isn't possible for someone to be negative years old but this is the answer that I obtained from the equations.

Hope this helps! :)
Have a lovely day! <3

Answer 2

n your problem, the son's current age is the smallest number so:

Let x = the son's current age

then 3x = the father's current age

and x+15 = the son's age in 15 years

and 3x+15 = the father's age in 15 years.

After we write the expressions we need to write equation(s). We need as many equations as the number of variables we've used. Since we were able to write all 4 expressions with just one variable, we will only need one equation. And we will write this equation using the only relationship we have not used already: "after 15 years, the father will be twice as old as his son at that time". In other words: The father's age in 15 years will be twice the son's age in 15 years. Using our expressions from above this sentence translates into:

3x + 15 = 2(x+15)

Once we have our equation(s) we solve them. Our equation is a fairly simple one to solve.

Simplify.

3x + 15 = 2x + 30

Subtract 2x from each side

x + 15 = 30

Subtract 15 from each side

x = 15

We can now use this solution to the equation and our expressions to answer the question: "The father's current age is ...". Since the expression for the father's current age was 3x, the answer is 3(15) = 45

As we can see, 45 is 3 times 15 and, in 15 years, 45+15 is the same as 2(15+15) so these numbers are correct.

I don't why 4, 5, 16, 32 or 64 are listed as possible solutions. In fact none of these numbers could have possibly been the answer since none of them is a multiple of 3 and the father's age would have to be a multiple of 3 since it is 3 times the son's age.