The answer is 10.
Parallel lines show similar triangles showing us that (2x + 6)/10 = (x+6)/8. Solving this equation for x gives us x = 2. Plugging this into 2x + 6 gives us 2(2) + 6 = 10.
Step-by-step explanation:
Let
= mass of the painter
= mass of the scaffold
= mass of the equipment
= tension in the cables
In order for this scaffold to remain in equilibrium, the net force and torque on it must be zero. The net force acting on the scaffold can be written as

Set this aside and let's look at the net torque on the scaffold. Assume the counterclockwise direction to be the positive direction for the rotation. The pivot point is chosen so that one of the unknown quantities is eliminated. Let's choose our pivot point to be the location of
. The net torque on the scaffold is then

Solving for T,

or
![T = \frac{1}{9}[m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m})]](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B1%7D%7B9%7D%5Bm_sg%281.9%5C%3A%5Ctext%7Bm%7D%29%20%2B%20m_pg%284.2%5C%3A%5Ctext%7Bm%7D%29%5D)

To solve for the the mass of the equipment
, use the value for T into Eqn(1):

Lets work out each set of brackets individually:
8 x 10 = 80
4 x 1 = 4
For the last bracket, note that: 2 times 1/100 is the same as 2 divided by 100
So:
2 x 1/100 = 2 ÷ 100
= 0.02
Now add up all of the numbers we worked out:
80 + 4 + 0.02 = 84 + 0.02
= 84.02
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Answer:
C. 84.02