The sum of two numbers is 10. Which of the following equations shows that the product of these two numbers is 21?

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 10. Since we don't know what the two numbers are, we will use variables (x and y) to represent them.
x+y=10
Next, we see that the product of these two numbers is 21, so we can also write out that equation for reference:
xy=21
Then, you isolate a variable in one equation. Let's isolate the y. We can start with the addition equation.
x + y = 10
In order to isolate y, we need to move x from the left hand side of the equation to the right hand side. To do this, we subtract x (since it's being added to the y) from both sides of the equation.
x - x + y = 10 - x
y = 10 - x
Therefore, we know that y is equal to 10 - x, so we can substitute it into the other equation in place of the y.
xy=21
x(10-x)=21
This is the final equation that represents "the product of the two numbers is 21."

The Sum of Two Numbers Is 10