Question 233484
let m = the mother's age.
let s = the son's age.


m = 5*s


Twice the age of the son is 3 years less than half of the mother's age.


2*s = (1/2)*m - 3


replace m from the first equation with 5*s in the second equation to get:


2*s = (1/2)*5*s - 3


multiply both sides of the equation by 2 to get:


4*s = 5*s - 6


subtract 4*s from both sides of the equation and add 6 to both sides of the equation to get:


s = 6


since m = 5*s, this makes m = 30


2 * 6 = 12


30/2 = 15 - 3 = 12


12 is twice the age of the son.
12 is half the mother's age minus 3


since they're the same, looks like we're good.


mother is 30 years old.
son is 6 years old.