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):
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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