Use a quadratic equation to find two real numbers with a sum of -15 and a product of -54

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Math and Arithmetic

What two numbers have a product of 54 and a sum of 15?

To find the answer to "What two numbers have a product of 54 and a sum of 15?" we first state what we know. We are looking for x and y and we know that x • y = 54 and x + y = 15. Before we keep going, it is important to know that x • y is the same as y • x and x + y is the same as y + x. The two variables are interchangeable. Which means that when we create one equation to solve the problem, we will have two answers. To solve the problem, we take x + y = 15 and solve it for y to get y = 15 - x. Then, we replace y in x • y = 54 with 15 - x to get this: x • (15 - x) = 54 Like we said above, the x and y are interchangeable, therefore the x in the equation above could also be y. The bottom line is that when we solved the equation we got two answers which are the two numbers that have a product of 54 and a sum of 15. The numbers are: 6 9 That's it! The two numbers that have a product of 54 and a sum of 15 are 6 and 9 as proven below: 6 • 9 = 54 6 + 9 = 15 Note: Answers are rounded up to the nearest 6 decimals if necessary so the answers may not be exact.

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Algebra.Com
Question 163242This question is from textbook Prentice Hall Mathematic Pre-Algebra
:

Find two whole numbers with a sum of 15 and a product of 54.

This question is from textbook Prentice Hall Mathematic Pre-Algebra

Found 2 solutions by checkley77, joecbaseball:Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!

x+y=15 or x=15-y xy=54 (15-y)y=54 15y-y^2=54 y^2-15y+54=0 (y-9)(y-6)=0 y-9=0 y=9 answer. y-6=0 y=6 answer.

Answer by joecbaseball(37) (Show Source): You can put this solution on YOUR website!
Call one whole number (integer) x, and the other y Then write two equations to represent what you are looking for: x + y = 15 x X y = 54 Solve any one of the equations in terms of one variable, and replace that value in the other equation. I will solve for x in the first equation: x = 15 - y Replacing the x in the second equation, we get that: (15-y)y = 54 Simplify the left hand side to get: 15y - y^2 = 54 Now, get the equation in terms of zero by subtracting 54 from both sides: 15y - y^2 � 54 = 0 Rearrange the terms to get in a nice form: y^2 -15y + 54 = 0 Factor this to get: (y-9)(y-6) = 0 Set each = 0 y � 9 = 0 ��. y = 9 y � 6 = 0 ��. y = 6 NOW� you have two values of y, but that is ok. The problem only asks for two whole numbers. If you substitute 9 into either equation for y, you get an x value of 6, AND If you substitute 6 into either equation for y, you get an x value of 9, Which is the same ! So, your answers are 9 and 6. Good luck! JoeC

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