Unemployment Rate

165,700,245.7

Let:
E = Employed Workers
U=Unemployed Workers

Labor Force Participation Rate = (E+U) / 70 Million = 67.44%

So, (E+U) = 70 Million * 0.6744 = 47,208,000. Or, stated another way:

E+U = 47,208,000

Since U = 10,000,000, that means E = 47,208,000 - 10,000,000 = 37,208,000. There are 37,208,000 Employed Workers.

How can 70m be less than 37m?

LFPR = 67.44%

70 million dont participate cant be greater than the work force if the work force is 67%

The unemployed would have to be 32.56%

LFPR must be greater than 70m.

70,000,000 Non-participants comprise 32.56% of the labour force , thus

144,987,715 Participants comprise 67.44% of the labour force

The 144,987,715 Participants are comprised of those that are employed and those that are looking for work ( aka the unemployed 10,000,000 )

Thus there are 134,987,715 employed.

Damn, I gotta stop doing calculations before I go to bed. I confused the non participants (70 M) with the Working Age Non-institutionalized Population.
Fobvius got it right.

Labor force Participation Rate = Labor Force ÷ Working Age Non-institutionalized Population
And Working Age Non-institutionalized Population = E + U + Non participants
Non participants, (70M) = 0.3256 of Non-institutionalizedWorking Age Population,
therefore Working Age Non-institutionalized Population = (1÷0.3256) * 70M = 3.0713 * 70M =214.9877M

Therefore E + 10M = 214.9877M * 0.6744
E + 10M = 144.9877
E = 144.9877M - 10M + 134.9877 M

80 million = 32.56 of x

260,480,000 employed persons