Problema Solution
Rachel is now four years older than her brother Ryan. Four years ago, Ryan was three-fifths his sister's age. In two years, Ryan will be three-fourths Rachel's age. How old are they now?
Answer provided by our tutors
let
x = the age of Rachel now
y = the age of Ryan now
Rachel is now four years older than her brother Ryan
x = y + 4
Four years ago, Ryan was three-fifths his sister's age
y - 4 = (3/5)(x - 4)
In two years, Ryan will be three-fourths Rachel's age
y + 2 = (3/4)(x + 2)
by solving the system
y - 4 = (3/5)(x - 4)
y + 2 = (3/4)(x + 2)
we find
x = 14
y = 10
click here to see the step by solution of the system of equations
Indeed Rachel is 4 years older the Ryan now (14 - 10 = 4)
Rachel is 14 years old now.
Ryan is 10 years old now.