SOLUTION: How do you find two whole numbers with a sum of 15 and a product of 54

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Question 407997: How do you find two whole numbers with a sum of 15 and a product of 54
Found 2 solutions by Edwin McCravy, MathLover1:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
How do you find two whole numbers with a sum of 15 and a product of 54
Make a list of all the pairs of whole numbers that 
have a product of 54:

1 x 54 = 54
2 x 27 = 54
3 x 18 = 54
6 x 9  = 54

Then make a list of their sums

1 + 54 = 55
2 + 27 = 29
3 + 18 = 21
6 + 9  = 15

And what do you know!  That last pair 6 and 9 do indeed
have a sum of 15.

Answer: 6 and 9

Edwin


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

find two whole numbers with a sum of 15 and a product of 54
let numbers be x and y
given:
a sum ofx and y is 15...
so, we have x%2By=15..........1
a product of x and y is 54
so, we have xy=54..........2

solve the system:
x%2By=15..........1
xy=54..........2
-----------------------------
x%2By=15..........1.solve for x
x=15-y..........1..substitute in 2

%2815-y%29y=54..........2...solve for y
15y-y%5E2=54
y%5E2-15y%2B54=0........
y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y+=+%28-%28-15%29+%2B-+sqrt%28+%28-15%29%5E2-4%2A1%2A54+%29%29%2F%282%2A1%29+

y+=+%2815+%2B-+sqrt%28225-216%29%29%2F2+
y+=+%2815+%2B-+sqrt%289%29%29%2F2+


y+=+%2815+%2B-+3%29%2F2+



y1+=+%2815+%2B3%29%2F2+
y1+=+%2818%29%2F2+

y1+=+9+

y2+=+%2815+-3%29%2F2+
y2+=+%2812%29%2F2+
y2+=+6

so, we have two solutions for y, and now we will find two solutions for x


x1=15-y...plug in y1
x1=15-9
x1=6

x2=15-y...plug in y2
x2=15-6
x2=9
the numbers x and y are x=6 and y=9 or x=9 and y=6