SOLUTION: The difference of two positive numbers is 9, and their product is 220. Find the two numbers.

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Question 685079: The difference of two positive numbers is 9, and their product is 220. Find the two numbers.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let's two positive numbers be x and y

The difference of two positive numbers is 9:
x-y=9........1
and their product is 220:
x%2Ay=220........2
solve the system:
x-y=9........1
x%2Ay=220........2
___________________________

x-y=9........1....solve for x
x=9%2By.......substitute in 2

%289%2By%29%2Ay=220........2...solve for y
9y%2By%5E2=220
y%5E2%2B9y-220=0.....use quadratic formula

y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

y+=+%28-9+%2B-+sqrt%28+9%5E2-4%2A1%2A%28-220%29+%29%29%2F%282%2A1%29+
y+=+%28-9+%2B-+sqrt%28+81%2B880+%29%29%2F2+
y+=+%28-9+%2B-+sqrt%28+961+%29%29%2F2+
y+=+%28-9+%2B-+31%29%2F2+
find only positive solution since numbers we are looking for are positive

y+=+%28-9+%2B+31%29%2F2+
y+=+22%2F2+
highlight%28y+=+11%29+

now find x

x=9%2By
x=9%2B11
highlight%28x=20%29