Question

Miss Lee had a certain number of muffins and cupcakes in her shop. If Miss Lee sold 60 muffins and 30 cupcakes each day, she would have 300 muffins left by the time she finished selling all her cupcakes. If Miss Lee sold 30 muffins and 60 cupcakes each day, she would have 930 muffins left by the time she finished selling all her cupcakes. Find the total number of muffins and cupcakes Miss Lee had in her shop.

Answer 1

Let's start by assigning variables to the numbers we want to find. m for muffins and c for cupcakes. Let's say the first selling statement takes a days, the second one takes b days.

m = 300 + 60a
c = 30a

m = 930 + 30b
c = 60b

Ok let's combine the first two equations so that a disappears:

2c = 60a
m = 300 + 2c

Now let's combine the last two equations so that b disappears:
c/2 = 30b
m = 930 + c/2

Now combine these results such that m disappears:

300 + 2c = 930 + c/2

... and simplify

3/2c = 630 => c = 420
m = 300 + 2*420 = 1140

So there were 420 cupcakes and 1140 muffins. 
a = 14 days, and b = 7 days, but that was not asked.