LCM and HCF

Question

Mrs Lim has 2 daughters, Helen and Melissa. The Highest Common Factor and Lowest Common Multiple is 3 and 168 respectively. If Helen is 3 years older than her sister, how old is Helen?

thanks in advance

Answer 1

x and x+3 are the ages

the product of the 2 numbers equals the HCF*LCM

x(x+3)=3*168

x^2+3x=504

x^2+3x-504=0

504=2*2*2*3*3*7=(2*2*2*3)*(3*7) and 24-21=3

factor

(x+24)(x-21)=0

x-21=0

x=21 years old

x+3=24 years old