Question 1168745
guess method.
given
unknowns
equations
setup
solve


given:
sherry is half as old as her mother.
twelve years ago, she was one third the age of her mother.
unknown:
what are both their ages now?
equations:
let s = sherry's age now.
let m = her mother's age now.
today she is half as old as her mother.
s = 1/2 * m
twelve years ago, she was one third the age of her mother.
s - 12 = 1/3 * (m - 12)
setup:
these are two equations that need to be solved simultaneously
they are:
s = 1/2 * m
s - 12 = 1/3 * (m - 12)
solve:
in the second equation, replace s with 1/2 * m from the first equation to get:
1/2 * m - 12 = 1/3 * (m - 12)
simplify to get:
1/2 * m - 12 = 1/3 * m - 4
add 12 to both sides of the equation and subtract 1/3 * m from both sides of the equation to get:
1/2 * m - 1/3 * m = -4 + 12
put everything on the left hand side of the equation under a common denominator to get:
3/6 * m - 2/6 * m = -4 + 12
simplify to get:
1/6 * m = 8
solve for m to get:
m = 8 * 6/1 = 48
solution:
sherry is 24 years old now and her mother is 48 years old now.
confirmation:
sherry is now 1/2 the age of her mother (24/48 = 1/2)
12 years ago, sherry was 12 and her mother was 36.
sherry was 1/3 the ages of her mother 12 years ago (12/36 = 1/3)