Age (could be tricky)

Question

David's age is ten years less than triple Joanna age. In five years, Joanna's age will be three-quarters of David's age. How old is each person now

Answer 1

D = 3J -10

 

J + 5 = 3/4 D

 

Solve these two simultaneous equations

 

plug in value of D from first equation in second equation

 

J + 5 = 3/4 ( 3J - 10) = 9/4 J - 30/4

 

J - 9/4 J = -30/4 - 5

 

-5/4 J = - 50/4

J = 10

D = 20

:) 

 

Answer 2

Let D = David's age and J = Joanna's age.

 

David's age is ten years less than triple Joanna age: D = 3J - 10

 

In five years, Joanna's age will be three-quarters of David's age: J+5 = (3/4)(D+5)

 

Substitute 3J-10 from the first equation for D in the second equation to find Joanna's age:

J+5 = (3/4)(D+5)

J+5 = (3/4)(3J-10+5)      [Substituted 3J-5 in place of D]

J+5 = (3/4)(3J-5)

J+5 = 9J/4 - 15/4

15/4 + 5 = 9J/4 - J

35/4 = 5J/4

 

Solve for J, Joanna's age.  Once you have J, David's age is D = 3J - 10.