SOLUTION: The product of two numbers is 39 their sum is 16 what is their difference?

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Question 303184: The product of two numbers is 39
their sum is 16
what is their difference?
Found 3 solutions by Fombitz, CharlesG2, Alan3354:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.AB=39
2.A%2BB=16
From eq. 1,
A=39%2FB
Substitute into eq. 2,
39%2FB%2BB=16
39%2BB%5E2=16B
B%5E2-16B%2B39=0
%28B-13%29%28B-3%29=0
Two solutions:
B-13=0
B=13
then
A=39%2F13=3
.
.
.
B-3=0
B=3
then
A=39%2F3=13
The two numbers are +3+ and 13.
The difference is either 10 or -10.

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
The product of two numbers is 39
their sum is 16
what is their difference?
A * B = 39
A + B = 16 --> A = 16 - B
A - B = ?
substitute in 16 - B for A in A * B = 39 and solve for B
(16 - B) * B = 39
16B - B^2 = 39
- B^2 + 16B - 39 = 0 (rearranging)
B^2 - 16B + 39 = 0 (dividing by -1)
(B - 3)(B - 13) = 0 (by FOIL equals above)
B = 3 or B = 13 so A = 13 or A = 3
A - B will be 13 - 3 = 10 or 3 - 13 = -10

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
You can do math, but if it's on a test it's good to save time.
39 has only 2 factors, 3 & 13
The difference is 10