SOLUTION: Please help me solve this equation. It says to define a variable, write an equation and solve each problem. The sum of two numbers is 25. Twelve less than four times one of the num

Algebra ->  Equations -> SOLUTION: Please help me solve this equation. It says to define a variable, write an equation and solve each problem. The sum of two numbers is 25. Twelve less than four times one of the num      Log On


   

Question 658304: Please help me solve this equation. It says to define a variable, write an equation and solve each problem. The sum of two numbers is 25. Twelve less than four times one of the numbers is 16 more than twice the other number. Find both numbers. I just don't know how to start by defining a variable.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
DEFINING ONE VARIABLE:
Let one of the numbers be x.

THE OTHER NUMBER:
The other number would be 25-x because the sum of the two numbers is 25.
Since you were asked to "define a variable," I assume that you are expected to use only one variable, and that saying that the other number is 25-x should be good enough.
If someone asked for proof of that, you could call the other number y, write that x%2By=25 and then solve for y to get that y=25-x.

TRANSLATING THE OTHER PIECE OF INFORMATION:
"Twelve less than four times one of the numbers is 16 more than twice the other number" talks about "one of the numbers" and "the other number."
Which of those numbers to call x is your choice.
I guess that choice is part of defining your variable.
The choice will determine the equation you end up with, but the end result will be the same.
You could chose to call the first number mentioned x.
In that case,
four times one of the numbers is 4x, and
twelve less than that is 4x-12.
The other number is 25-x.
Twice the other number is 2%2825-x%29, and
16 more than that is 2%2825-x%29%2B16.
"Twelve less than four times one of the numbers is 16 more than twice the other number" translates as
4x-12=2%2825-x%29%2B16.

SOLVING THE EQUATION:
4x-12=2%2825-x%29%2B16 --> 4x-12=2%2A25-2x%2B16 (applying the distributive property)
4x-12=2%2A25-2x%2B16 --> 4x-12=50-2x%2B16 --> 4x-12=66-2x (performing indicated operations, collecting like terms)
4x-12=66-2x --> 4x-12%2B12=66-2x%2B12 --> 4x=78-2x
4x=78-2x --> 4x%2B2x=78-2x%2B2x --> 6x=78
6x=78 --> 6x%2F6=78%2F6 --> highlight%28x=13%29
The other number is 25-13=highlight%2812%29

VERIFICATION:
12%2B13=25
4%2A13-12=2%2A12%2B16 because
4%2A13-12=52-12=40 and 2%2A12%2B16=24%2B16=40