Question 218792
This is a ratio problem
Let {{{r}}} = Rita's age
Let {{{s}}} = Sister's age
The thing to notice here, is that with any 2 people,
the difference in their ages will always be the same,
but one will only be twice the other's age at one time
in their lives.
Say I'm 20 and you're 10. In one year the ratio is
{{{21/11 = 1.909}}}, no longer {{{2}}}
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The difference in Rita's and her Sister's ages (always) is
{{{8 - 4 = 4}}} or,
{{{s = r - 4}}}
So, I can state that
{{{r/s = 1.25/1}}}
{{{r/(r-4) = 1.25/1}}}
Multiply both sides by {{{r-4}}}
{{{r = 1.25*(r-4)}}}
{{{r = 1.25r - 5}}}
{{{.25r = 5}}}
{{{r = 5/.25}}}
{{{r = 20}}}
{{{s = 16}}} (since {{{s = r - 4}}})
Rita will be 20 when she is {{{1.25}}} times as old as her sister