To find how old Mrs. Roberts was when her son was born, we first need to know both of their ages. I'm going to give #"Mrs. Roberts"# the variable #m# and her #"son"# the variable #s#.
Let's turn the two sentences about their ages into equations:
#stackrel(m)overbrace"Mrs. Roberts"stackrel(=)overbrace"is"stackrel(3s)overbrace"three times as old as her son"#
#color(blue)(m = 3s)#
#stackrel(m + s)overbrace"the sum of their ages"stackrel(=)overbrace"is"stackrel(48)overbrace"48"#
#color(blue)(m + s = 48)#
Now substitute the first equation into the second one:
#m + s = 48#
#(3s) + s = 48#
#4s = 48#
#s = 12#
The son is #12# years old. Now substitute #s# into one of the equations to solve for the mother's age:
#m = 3s#
#m = 3(12)#
#m = 36#
Mrs. Roberts is #36#. Since they are asking how old she was when her son was born, we will subtract her son's age from her age, since she would be #12# years younger:
#36 - 12 = 24#
Mrs. Roberts was #24# when her son was born.
