Question

What numbers when multiplied equals 1800 but when adding equals 105

Answer 1

let x = first number
y = second number

(1) xy = 1800

(2) x + y = 105
y = 105 - x
we will substitute y to the first equation

(1) (x)(105 - x) = 1800

`105x - x^2 - 1800 = 0`

`x^2 - 105x + 1800 = 0`
Using formula
`\frac{-b+ \sqrt{ b^(2) -4ac} }{2a}`
a = 1, b = -105, c = 1800

`\frac{-(-105)+ \sqrt{ (-105)^(2)- 4(1)(1800) } }{2(1)}` = x

`(105+ √(11025-7200) )/(2) =x`

`(105+61.85)/(2) = x`

`(166.85)/(2) =x`

`x=83.43`

(2) x + y = 105
we'll substitute x = 83.43
83.43 + y = 105
y = 105 - 83.43
y = 21.57

Therefore, the two numbers are 83.43 and 21.57