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

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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