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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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

Explanation:

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

$S : B = 4 : 1$ $S:B = 4:1$

$\Rightarrow 4 B = S$ $=> 4B = S$

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

$\Rightarrow S + 20 = 2 (B + 20)$ $=> S + 20 = 2(B + 20)$

$4 B = S$ $4B = S$

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

$\Rightarrow 4 B + 20 = 2 B + 40$ $=> 4B + 20 = 2B + 40$

$\Rightarrow 2 B = 20$ $=> 2B = 20$
$\Rightarrow B = 10$ $=> B = 10$

$\Rightarrow S = 4 B = 40$ $=> S = 4B = 40$

Answer 2 · 2016-10-31T11:05:46

Sue is $40$ $40$ and Betty is $10$ $10$

Explanation:

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

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

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

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

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

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

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

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

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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?

2 Answers

Explanation:

Explanation:

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