SOLUTION: 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

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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