Working simultaneously and independently at an identical constant rate, 5 machines of a certain type can produce a total of x units of product P in 8 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
Choose the correct choice from the following choices:
A) 30	B) 18	C) 16	D) 12	E) 8

Rationale: 5 machines do x units in 8 days we have x / 8 = > rate of the 5 machines we know that we need to have 3 x units in 4 days therefore , we need to get to 3 x / 4 rate of the machines . rate of one machine is x / 8 * 1 / 5 = x / 40 . now , we need to know how many machines need to work simultaneously , to get 3 x done in 4 days . 3 x / 4 work needs to be done by machines that work at x / 40 rate . let ' s assign a constant y for the number of machines : ( x / 40 ) * y = 3 x / 4 y = 3 x / 4 * 40 / x cancel 4 with 40 , and x with x and get - > 30 . answer choice a
Answer: A