Question 657207
Divide and conquer. Working one piece of the problem at a time, you need to read, interpret, and write as equations the pieces of information given.
 
I would start by defining a variable, like this:
Let {{{x}}} be Sara's age (in years, of course).
 
"Ashley's is 9 years less than twice Sara's age."
Twice Sara's age would be {{{2x}}}, and 9 years less than that
would be {{{2x-9}}}.
So, Ashley's age is {{{2x-9}}}.
 
"The sum of 8 times Sara's age and 5 times Ashley's age" involves
8 times {{{x}}}, which is {{{8x}}} and
5 times {{{2x-9}}}, which is {{{5(2x-9)}}}.
The sum of those two numbers is 81, which means
{{{highlight(8x+5(2x-9)=81)}}}.
That is your equation.
 
Now, we solve:
First, we simplify the equation a bit.
To get rid of a parenthesis that is multiplied by a number (or an expression), we use the distributive property:
{{{8x+5(2x-9)=81}}} --> {{{8x+5*(2x)+5*(-9)=81}}} --> {{{8x+10x-45=81}}} --> {{{18x-45=81}}}
From there, we solve:
{{{18x-45=81}}} --> {{{18x-45+45=81+45}}} --> {{{18x=126}}} (adding 45 to both sides of the equal sign)
{{{18x=126}}} --> {{{18x/18=126/18}}} --> {{{highlight(x=7)}}} (dividing both sides by 18)
 
Now we can translate the algebra back into words.
Sara is {{{highlight(7)}}}.
We said above that Ashley's age was {{{2x-9}}}, so
Ashley's age is {{{2*7-9=highlight(5)}}}.
 
The sum of 8 times Sara's age and 5 times Ashley's age is
{{{8*7+5*5=56+25}}} and {{{56+25=81}}}.