The difference between two numbers is twice as large as 2. The two numbers multiplied together is then divided by two and the result is 16. Which of the following expresses this?

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Quizplus · Accepted Answer

When doing problems like this, the best way to ensure you do not make any mistakes is to create your own variables and different equations for each piece of information you are given. Then you can combine the equations.
Start with the statement that the difference between two numbers is twice as large as 2. Since we don't know what the two numbers are, we will use variables (x and y) to represent them. We also are told that the difference between two numbers is twice as large as two.
x - y = 2 (2)
so
x - y = 4
Then, you isolate a variable in one equation. Let's isolate the y. We can start with the subtraction equation.
x - y = 4
In order to isolate y, we need to move x from the left hand side of the equation to the right hand side. In order to avoid having our y be negative, we will do this in two steps.
First, we will add the y to the right hand side of the equation, making it positive.
x - y + y = 4 + y
x = 4 + y
Now, we subtract the 4 from both sides in order to move it over to the left hand side of the equation and isolate the y.
x - 4 = 4 - 4 + y
x - 4 = y
Therefore, we know that y is equal to x - 4, so we can substitute it into the other equation in place of the y.
The second equation should show the two numbers multiplied together is then divided by two and the result is 16.
(xy) ÷ 2 = 16
Now we substitute x - 4 for y in the other equation:
x (x - 4) ÷ 2 = 16
Finally, in order to isolate all of the variables, we want to move the 2 over to the right hand side of the equation. We do this by multiplying both sides by 2, since the left hand side is being divided by 2.
x (x - 4) ÷ 2 • 2 = 16 • 2
x (x - 4) = 32

The Difference Between Two Numbers Is Twice as Large as 2