The sum of two numbers is 15. Their product is 56. Find the numbers

Answer 1

Factors of 56:

8 x 7 8 + 7 =15

2 x 28

4 x 14

etc.

The two numbers are 8 & 7

Answer 2

You can also solve the problem without looking at the factors of 56...

Equation 1 : A*B = 56

Equation 2 : A + B = 15

Solve for A or B in one of the equations and plug the solution into the other equation... I'll solve for A using the 2nd equation

A + B = 15

subtract B from both sides

A = 15 - B

Plug solution into the 1st equation

A*B = 56

(15 - B)*B = 56

15B - B² = 56

subtract (15B - B²) from both sides and reorganize.... (I did it that way so the B² coefficient is positive)

B² -15B + 56 = 0

solve via quadratic equation

[ -b ± √(b² - 4ac) ] / 2a

[ 15 ± √(1) ] / 2

Roots are : 7 & 8

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You could also of done it the other way...

I'll solve for A using the 1st equation :

A*B = 56

Divide by B

A = 56/B

Plug into the 1st equation :

A + B = 15

56/B + B = 15

Multiply both sides by B

56 + B² = 15B

reorganize...

B² -15B + 56 = 0

and you have the same thing we had doing it the other way...

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Check your work!!

Answers are 7 & 8

Equation 1 : A*B = 56

7 * 8 = 56 correct

Equation 2 : A + B = 15

7 + 8 = 15 correct