SOLUTION: please help me solve this problem:Rose is 6 years older than his sister Cora in 4 years she will be 9 years more than 1/2 as old as Cora. how old are the girls now?

Question 1058442: please help me solve this problem:Rose is 6 years older than his sister Cora in 4 years she will be 9 years more than 1/2 as old as Cora. how old are the girls now?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= Cora's age now
= Rose's age now.
In 4 years, Cora's age will be ,
and Rose's age will be .
The problem says that will be
9 more than half Cora's age,
which would be
.
So,our equation is
.
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."
= Cora's age
= Rose's age

Cora is
and Rose is .

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 to .
Applying the distributive property, that is
.
Then,I simplify that to
and then to
and to .
I do not write all those baby steps,
I just do them in my head.
In the next step,
I add 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.
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