Question 1058442
{{{x}}}= Cora's age now
{{{x+6}}}= Rose's age now.
In 4 years, Cora's age will be {{{x+4}}} ,
and Rose's age will be {{{x+6+4}}} .
The problem says that will be
9 more than half Cora's age,
which would be
{{{(x+4)/2+9}}} .
So,our equation is
{{{x+6+4=(x+4)/2+9}}} .
There are many different paths to the solution.
Solve that equation whatever way feels comfortable to you.
This is how I would "show my work."
{{{x}}}= Cora's age
{{{x+6}}}= Rose's age
{{{x+6+4=(x+4)/2+9}}}
{{{x+10=(x+4)/2+9}}}
{{{2x+20=x+4+18}}}
{{{2x+20=x+22}}}
{{{2x-x=22-20}}}
{{{x=2}
{{{x+6=2+6}}}
{{{x+6=8}}}
Cora is {{{highlight(2)}}}
and Rose is {{{highlight(8)}}} .
 
Checking: In 4 years, Cora will be 6 and Rose will be 12.
Half of Cora's age will be 3, and 9 more than that will be 12.
 
Explanation for my equation solving steps:
To "eliminate denominators" I multiplied both sides of the equal sign times the 2 that appeared in the denominator.
In baby steps, that would take me
from {{{x+10=(x+4)/2+9}}} to {{{2*(x+10)=2*((x+4)/2+9)}}} .
Applying the distributive property, that is
{{{2x+2*10=2*((x+4)/2)+2*9}}} .
Then,I simplify that to
{{{2x+20=(x+4)+18}}} and then to
{{{2x+20=x+4+18}}} and to {{{2x+20=x+22}}} .
I do not write all those baby steps,
I just do them in my head.
In the next step,
I add {{{-x-20}}} to both sides of the equation,
or subtract x and 20 from both sides of the equation,
to have all the x's on one side and a'll the numbers without x's on the other.
I could have done that in two steps
if I had a teacher who liked it better that way.