Question

the product of two negative numbers is 160. if the lesser of the two numbers is 4 less than twice the greater, what is the greater number?

Answer 1

The greater number is
`- 8`

Explanation:

Let the numbers be x and y

We have x · y = 160

x= 160/y

let x be the smaller number

x = 2y - 4

x - 2y = -4

Substitute x = 160/y in the above equation

160/y - 2y = -4

Multiply throughout by y
160 - 2y² = -4y

Add 4y to both sides

160 - 2y² + 4y = 0

Rearrange

-2y² + 4y + 160 = 0

Divide by -2

y² - 2y + 80 = 0

Factor expression on left side

(y - 10)(y + 8) = 0

y - 10 = 0 ==> y = 10

y + 8 = 0 ==> y = -8

Since both numbers are negative y = -8

So the greater number is - 8

The lesser number = 160/y = 160/-8 = -20

Remember that both numbers are negative and -20 < -8