Question 201720
sue is now 7 times as old as louise.
let x = sue's age now.
let y = louise's age now.
x = 7 * y
in 6 years sue will be x + 6 years old.
in 6 years louise will be y + 6 years old.
in 6 years sue will be 5 times as old as louise.
x + 6 = 5 * (y + 6)
simplify to get
x + 6 = 5*y + 30
subtract 6 from both sides of the equation and subtract 5*y from both sides of the equation to get
x - 5*y = 30 - 6
which becomes
x - 5y = 24
since x = 7y (from above) we get
7y - 5y = 24
simplify to get
2y = 24
divide both sides by 2 to get
y = 12
since y is louise's age now, then louise is 12 years old now.
since sue is 7 times as old as louise now, then sue is 84.
in 6 years from now sue will be 90 and louise will be 18.
sue will be 5 times as old as louise.
everything checks out.
x = sue's age now = 84
y = louise's age now = 12.