Question 657207: will you please help me solve this problem, I am not even sure how to start working it out, i cant even figure how to write an equation for this problem. please help: "the sum of 8 times Sara's age and 5 times Ashley's age is 81. Ashley's is 9 years less than twice Sara's age. Find the age of each girl."
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 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  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  , and 9 years less than that
would be  .
So, Ashley's age is .
"The sum of 8 times Sara's age and 5 times Ashley's age" involves
8 times , which is  and
5 times , which is  .
The sum of those two numbers is 81, which means
 .
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:
 -->  -->  --> 
From there, we solve:
-->  -->  (adding 45 to both sides of the equal sign)
-->  -->  (dividing both sides by 18)
Now we can translate the algebra back into words.
Sara is  .
We said above that Ashley's age was , so
Ashley's age is  .
The sum of 8 times Sara's age and 5 times Ashley's age is
 and  .
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