The cupcake factory sells cupcakes in three different types of packages. The first type is a 3-pack. The second type is a 6-pack. The third type is a 9-pack.

Part 1:

The cupcake factory has 810 cupcakes to package. The company's leaders want to divide the cupcakes so that an equal number of cupcakes will be put into the 3 different types of packages. How many cupcakes will go into each type of package?

3-pack = 135 cupcakes

6-pack = 270 cupcakes

9-pack = 405 cupcakes

Step-by-step explanation:

Let's say that 3-pack = a, 6-pack = b and 9-pack = c

The company's leaders want to divide the cupcakes so that 3-pack, 6-pack and 9-pack packages produced are the same. This translate to an equation of:

a=b=c

The factory has 810 cupcakes in total. The equation will be:

a*3 + b*6 + c * 9 = 810

3a + 6b + 9c = 810

If we substitute the 1st equation into the second (we can put b=a and c=a), the equation will become

3a + 6b + 9c = 810

3a + 6 (a) + 9 (a) = 810

18a = 810

a=45

Using the first equation, we know that we have 45 packages of each kind.

If there are 45 packages of 3-pack, the number of cupcakes go into 3-package will be: 3*45 = 135 cupcakes

If there are 45 packages of 6-pack, the number of cupcakes go into 6-package will be: 6*45 = 270 cupcakes

If there are 45 packages of 9-pack, the number of cupcakes go into 9-package will be: 9*45 = 405 cupcakes