Working at their respective constant rates, machine a makes 100 copies in 12 minutes and machine b makes 150 copies in 10 minutes. if these machines work simultaneously at their respective rates for 30 minutes, what is the total number of copies that they will produce? (a) 250 (b) 425 (c) 675 (d) 700 (e) 750

Since both machines maintain their rate, the number of copies made and the elapsed time are proportional. This means that we can write a proportion like

We know the performance of machine a for 12 minutes, and we want those for 30 minutes: the proportion becomes

Similarly, we have for machine b

So, together, the two machines make

copies.