Question 262682
f = father's age.
s = son's age.


the father is 30 years older than his son.


f = s + 30


in 5 years, the father will be 3 times as old as his son.


f + 5 = 3 * (s+5)


what is the father's age?


solve these 2 equations simultaneously to get your answer.


solve for f in terms of s in the first equation.   


this is already done because the equation states that:


f = s + 30


substitute for f in the second equation.


second equation is:


f + 5 = 3 * (s + 5)


equation becomes:


s + 30 + 5 = 3 * (s + 5)


simplify to get:


s + 35 = 3*s + 15


subtract s from both sides of this equation and subtract 15 from both sides of this equation to get:


20 = 2*s


divide both sides of this equation by 2 to get:


s = 20/2 = 10


from the first equation, we get:


f = s + 30 becomes f = 10 + 30 becomes f = 40


we have:


f = 40
s = 10


substitute f = 40 and s = 10 in both original equations to see if they are true.


f = s + 30 becomes 40 = 10 + 30 becomes 40 = 40 which is true.


f + 5 = 3 * (s + 5) becomes 40 + 5 = 3 * (10 + 5) becomes 45 = 30 + 15 becomes 45 = 45 which is also true.


both equations are true confirming the values for f and s of 40 and 10 are good.