What is the difference between a theorem and a proof

it should be C

Step-by-step explanation:

proof is (countable) an effort, process, or operation designed to establish or discover a fact or truth; an act of testing; a test; a trial while theorem is (mathematics) a mathematical statement of some importance that has been proven to be true

its line 2 i just added the rest or else it wouldn't let me answer

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.