Question 954817
S=Sophie's age; G=Grandmother's age
G=4S
G-1=5(S-1) Substitute for G
4S-1=5(S-1)
4S-1=5S-5 Subtract 4S from each side.
-1=S-5 Add 5 to each side.
4 years=S
G=4S=4(4)=16 years
G+S=4yrs+16yrs=20 yrs ANSWER The sum of their ages is 20 years.
CHECK:
Grandmother is four times as old as Sophie:
G=4S
16 years=4(4yrs)
16 yrs=16 yrs
Last year, Grandmother was 3 times as old:
G-1=5(S-1)
16yrs-1=5(4yrs-1)
15 yrs=5(3 yrs)
15 yrs=15 yrs