Question

The sum of two numbers is 19 and the prouduct is 78 what is the smaller number

Answer 1

let one number be x
then the other be 19-x
x(19-x) = 78
19x - x^2 = 78
x^2 - 19x + 78 = 0
(x-6)(x-13) = 0
x = 6 or x = 13

so the smaller is 6, the larger is 19-6 or 13

Answer 2

s = smaller number

l = larger number

s + l = 19

Subtract s to both sides.

l = 19 - s

s • l = 78

s ( 19 - s ) = 78

19 s - s² = 78

Subtract 78 to both sides.

- s² + 19 s - 78 = 0

Multiply both sides by - 1

s² - 19 s + 78 = 0

The solutions are:

s = 6 and s = 13

For s = 6

l = 19 - s = 19 - 6 = 13

For s = 13

l = 19 - s = l = 19 - 13 = 6

A larger number cannot be less than a smaller number.

That's why the larger number = 13

The smaller number = 6