Working simultaneously and independently at an identical constant rate, 6 machines of a certain type can produce a total of x units of product P in 10 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 5x units of product P in 6 days?
Choose the correct option.
A) 50	B) 18	C) 16	D) 12	E) 8
6 machines do x units in 10 days   we have x/10 =&gt; rate of the 6 machines   we know that we need to have 5x units in 6 days   therefore, we need to get to 5x/6 rate of the machines.   rate of one machine is x/10*1/6 = x/60.   now, we need to know how many machines need to work simultaneously, to get 5x done in 6 days.   5x/6 work needs to be done by machines that work at x/60 rate.   let's assign a constant Y for the number of machines:   (x/60)*y = 5x/6   y = 5x/6 * 60/x   cancel 6 with 60, and x with x and get -&gt; 50. 50nswer choice 50
<result>A</result>
Working simultaneously and independently at an identical constant rate, 6 machines of a certain type can produce a total of x units of product P in 10 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 5x units of product P in 6 days?