Elementary Algebra Help!

Question

One number is six more than two times another. If their sum is decreased by two, the result is nineteen. Find the numbers.

Answer 1

Hi Josie.

For word problems need to be able to "translate" English words into math operations.

 

So "more than" is usually adding.

"times" is usually multiplying

"sum" is adding

"decreased" is subtracting

"result is" is EQUAL (=)

"is" is EQUAL (=)

 

So let's translate the sentences into "math speak".

 

First we need to call the numbers something.  NUM1  and NUM2  work, but x and y are easier to write.

I will let one of the numbers be x, and the other be y.

 

"One number is six more than two times another"

            x        =  6      +       2*y

 

or 

x=6+2y

 

 

"If their sum is decreased by two, the result is nineteen.
Sum is x+y, so this translates to

 

       x+y - 2 = 19

 

 

So now you have a "System of Equations":

 

x=6+2y

x+y-2=19

 

 

Substitute the top expression for x into the bottom equation.

 

(6+2y) + y - 2 = 19

 

Add 2 to both sides

 

6+2y+y=21

 

Combine like terms (2y+y=3y) and subtract 6 from both sides

 

3y=15

 

Divide both sides by 3 and find that y=5.

 

Since we know that x = 6 + 2y, we can put 5 in for every y, and find that

 

x=6+2(5)=6+10=16

 

So our two numbers are:

 

16 and 5