Question 1058440
Please help me solve this problem:

Rose is 6 years older than her sister Cora.

{{{R}}}{{{""=""}}}{{{C+6}}}
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In 4 years she will be 9 years more than 1/2 as old as Cora.  
<pre>
{{{R+4}}}{{{""=""}}}{{{expr(1/2)(C+4)+9}}}

Simplify:

Multiply through by 2 to clear the fraction:

{{{2R+8}}}{{{""=""}}}{{{(C+4)+18}}}

{{{2R+8}}}{{{""=""}}}{{{C+4+18}}}

{{{2R+8}}}{{{""=""}}}{{{C+22}}}

{{{2R}}}{{{""=""}}}{{{C+14}}}

Since {{{R}}}{{{""=""}}}{{{C+6}}},

we substitute:

{{{2(C+6)}}}{{{""=""}}}{{{C+14}}}

{{{2C+12}}}{{{""=""}}}{{{C+14}}}

{{{C}}}{{{""=""}}}{{{2}}}

Since {{{R}}}{{{""=""}}}{{{C+6}}}, we substitute:

{{{R}}}{{{""=""}}}{{{2+6}}}

{{{R}}}{{{""=""}}}{{{8}}}.

So now, Rose is 8 and Cora is 2.

Checking:

Rose is 8, and that is 4 times Cora's age, which is 2.

That checks.

In 4 years Rose will be 12, and Cora will be 6.

12 is 9 more than 3 and 3 will then be half of
Cora's age, which will then be 6.

That also checks.

Edwin</pre>