# The product of two negative numbers is 160. If the lesser of the two numbers…

# Solution:

We are given that the product of two negative numbers is 160 and that the lesser of the two numbers is 4 less than twice the greater.

We can let x = the larger number and y = the smaller number, and we can create the following equations:

(x)(y) = 160

AND

y = 2x – 4

Substituting (2x – 4) for y in the first equation yields:

x(2x – 4) = 160

2x^2 + 4x = 160

x^2 – 2x – 80 = 0

(x – 10)(x + 8) = 0

x = 10 or x = -8

Since x is negative, x = -8 and y = 2(-8) -4 = -20.

Thus, the greater number is -8.

**Answer: D**