Question

Five years ago Katie was ten times as old as her daughter Melanie was. In 15 years
Katie will be three times as old as Melanie will be in 11 years. Use simultaneous
equations to determine Katie and Melanie’s current ages.

Answer 1

let Katie's present age be k
let Melanie's present age be m

Five years ago:
Katie ---- k - 5
Melanie -- m-5

k-5 = 10(m-5)
k - 10m = -45 **

2nd condition:
Katie's age in 15 years = 3(Melanies age in 11 years)
k + 15 = 3(m + 11)
k+15 = 3m + 33
k - 3m = 18 ***

subtract ** from ***
7m = 63
m = 9
in ** , k - 90 = -45
k = 45

Katie is now 45 years old and Melanie is now 9.

check:
5 years ago, Melanie was 4 and Katie was 40
10 times as old? YES, check!
in 15 years, Katie will be 60
in 11 years Melanie will be 20.
3 times as old? YES, Check!

Answer 2

Thank you so much Reiny. I have spent 2 hours looking at this and it has driven me crazy. I really need some practice in unravelling the questions!