Word Problem

Question

Ethan's father is x² years old while Ethan is x years old. In 4x years' time, Ethan father will be twice as old as him.

 

i.Form an equation in x and show that it reduces to x²-6x=0

ii. Solve the equation x²-6x=0.

iii. Find the age of Ethan father when Ethan was born.

 

Answer 1

Hi Andrew

 

When Ethan is X then his father is X²

 

When you add 4X years to Ethan he is X+4X but his father is now 2 times that so he is 2(X+4X) but he is also X² +4X so these 2 equations are equal:

 

X² + 4X = 2(X+4X)

X² + 4X = 2X + 8X

X² + 4X = 10X

X² - 6X = 0

X(X-6) = 0

X = 0 is not an answer because when Ethan is 0 years old his father can't be 0 years old also

X= 6 is an answer because when Ethan is 6 years old his father is 36 years old and when Ethan was born his father was 30

 

All the best

 

Lori