Form a system of equations to solve the problem. The sum of two numbers is 12. The difference of the numbers is 5. What is the smaller of the two numbers?

Question

Hey, having an issue with this problem. Hopefully someone can figure it out! Thanks so much!

Answer 1

Hello, Ella,

First, underline or highlight key words and numbers in the problem: 

 

Let one number = x   and the other number number=y   "Sum"  is addition of the numbers

          x+y                       = 12                           x-y                      = 5

The sum of two numbers is 12.  The difference of the numbers is 5. 

                   x+y=12            

                   x-y=5         Add the equations together to eliminate a variable, such as "y." Solve for "x."

 

Then you will be able to see which is smaller of the two numbers.

 

Q:  What is the smaller of the two numbers?

 

I will let you finish the problem.  I hope that my example has helped.  Susan C.

Answer 2

Let x = number1

Let y = number2

 

Then:   x + y = 12

and      x - y  = 5

 

Add the second equation to the first equation to get:

 

2x + 0 = 17.

 

Solve for x by dividing both sides by 2 to get x as follows:

 

(2x)/2 = 17/2

x = 17/2.

 

Now substitute 17/2 into either equation.  Let's substitute into the problem with addition since addition is easier to work with.

 

17/2 + y = 12

 

Now solve for y by subtracting 17/2 from both sides of the equation.

 

17/2 -17/2 + y = 12 - 17/2

 

You'll see that the left side simplifies to y.  To simplify the right side of the equation, we'll need to force a common denominator of 2 by multiplying the 12 on the right side by 2/2.  The result of both actions is:

 

y = 12 * (2/2) - 17/2

y = 24/2 - 17/2

y = 7/2

 

The smaller of 17/2 and 7/2 is 7/2 or 3.5.

Answer 3

Try to turn the sentences into "mathematical sentences."

 

The sum of two numbers is 12 -- This is "x + y = 12", since the "sum of two numbers is "x + y", and "is" means an equal sign.

 

The difference of the numbers is 5 -- This is "x - y = 5", since the "difference of the numbers is "x - y".

 

Therefore, your system of equations is:

 

x + y = 12

x - y = 5

 

Solve the system using the substitution method or elimination method to solve for x and y.