The ratio of Sue's age to Betty's age is 4:1. Twenty years from now, Sue will be twice as old as Betty will be then. How do you find their present age?

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Answer 1 · 2016-10-31T10:58:34

Betty: 10
Sue: 40

Let #S# be Sue's age
Let #B# be Betty's age

#S:B = 4:1#

#=> 4B = S#

#S + 20:B + 20 = 2:1#

#=> S + 20 = 2(B + 20)#

#4B = S#

#S + 20 = 2(B + 20)#

#=> 4B + 20 = 2B + 40#

#=> 2B = 20#
#=> B = 10#

#=> S = 4B = 40#

Answer 2 · 2016-10-31T11:05:46

Sue is #40# and Betty is #10#

Let Sue's current age be #S#
and Betty's current age be #B#

The ratio of Sue's age to Betty's age is #4:1#
#rarr S/B=4/1color(white)("XX")orcolor(white)("XX")S=4Bcolor(white)("XX")#[1]

Twenty years from now Sue will be twice as old as Betty.
#rarr S+20 = 2xx(B+20)color(white)("XXXX")#[2]

Substituting #4B# for #S# (from [1]) into [2]
#color(white)("XXX")4B+20=2(B+20)#

#color(white)("XXX")4B+20=2B+40#

#color(white)("XXX")2B=20#

#color(white)("XXX")B=10#

Substituting #10# for #B# back in [1]
#color(white)("XXX")S=4xx10=40#