The sum of two numbers is 4. Which of the following equations shows that twice the product of these numbers is equal to 35?

Question

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 sum of two numbers is 4. Since we don't know what the two numbers are, we will use variables (x and y) to represent them. x + y = 4 Then, you isolate a variable in one equation. Let's isolate the y. We can start with the addition 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. We do this by subtracting the x from both sides, since it is being added to the y. x - x + y = 4 - x Therefore, we know that y is equal to 4 - x, so we can substitute it into the other equation in place of the y. The second equation should show that twice the product of the two numbers is equal to 35. 2xy = 35 Now we substitute 4 - x for y in this equation: 2 • x • (4 - x) = 35 Begin to simplify by multiplying the two terms outside of the parentheses. 2x (4 - x) = 35 Distribute the 2x to both values inside of the parentheses. (2x • 4) - (2x • x) = 35 8x - 2x² = 35

The Sum of Two Numbers Is 4