A baker has small and large bags of sugar for making cakes. The large bag contains 30 cups cups of sugar and is 2.5 times larger than the small bag. The small bag contains enough sugar to make 9 cakes and have 0.75 cups of sugar remaining. How many cakes can be made with a large bag of sugar?

Step-by-step explanation:

The first thing we need to focus on is the fact the large bag (30 cups) is 2.5 larger than the small bag. So, the first we need to do is divided 30 by 2.5, which is 12. (300/25 = 30/2.5 = 12, in case you're confused.) So the small bag has 12 cups of sugar.

What that down, we need to focus how many cakes the small bag can make, which was 9. 3/4 of a cup is left over. We can create an equation from that info, that being 9x + 0.75 = 12. Now let's solve for x.

9x + 0.75 = 12

First, subtract 0.75 from both sides. With that, we can solve for x directly.

9x = 12 - 0.75

9x = 11.25

Now, divide both sides by 9.

x = 11.25/9

x = 1.25

With that, we now know that each cake needs 1.25 cups of sugar.

With that, the last thing we need to is divide 30 by 1.25. Again, I can use powers of ten, to quickly divide 3000 by 125 (10²) to get 24 cakes.

With that done, we have our answer. 24 cakes can be made with a large bag of sugar.

I hope this helps!  (⌒ω⌒)