Question

Five years ago, a father was 3 times as old

as his son, now their combined ages amount
to 110 years. How old are they?

Answer 1

The son is currently 30 years old, and the father is 80 years old. We used the provided relationships about their ages five years ago and their combined current ages to set up and solve a system of equations.

Step-by-step explanation:

The question involves solving a system of equations based on the given age relationship between a father and his son and their combined current ages.

Let's define the son's age five years ago as 's' and the father's age at that time as 'f'. The problem states that five years ago, the father was three times as old as his son, giving us the equation:

f = 3s.

It also states that their current combined ages are 110 years. If s + 5 is the son's current age and f + 5 is the father's current age, then:

s + 5 + f + 5 = 110,

which simplifies to:

s + f + 10 = 110.

Now going back to our first equation where f = 3s, we can substitute the value of f into the second equation:

s + (3s) + 10 = 110.

Combining like terms gives us 4s + 10 = 110, and solving for 's' gives s = 25. Therefore, the son's current age is 25 + 5 = 30 years, and the father's current age is 3(25) + 5 = 80 years.

Answer 2

Father is 80 years old and the son is 30

Step-by-step explanation:

Let father be x and son be y:

x-5 = 3(y-5)

x = 3y-10 ------ eq1

x+y = 110

x = 110 -y -------- eq2

Now if we combine the 2 equations we get:

3y + y = 110+10

y=30 (sons age)

Substituting in equation 2 we get:

x = 110 - 30

x = 80

Therefore, the fathers age is 80 and the sons age is 30.