Determine the number of solutions that exist for the given equation.

0.75 (x + 40) = 0.35 (x + 20) + 0.35 (x + 20)

First, distribute the numbers outside the parentheses with those inside. That would be,

0.75x + 30 = 0.35x + 7 + 0.35x + 7

Simplifying,

0.75x + 30 = 0.70x + 40

The value of x from the equation is 200. Thus, the equation only has 1 solution and that is 200.

0.75 (x + 40) = 0.35 (x + 20) + 0.35 (x + 20)

0.75x + 30 = 0.35x + 7 + 0.35x + 7

0.75x = 0.70x + 14 - 30

0.75x - 0.70x = - 16

0.05x = - 16

x = - 16/0.05

x = - 320

one solution