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

45 degres

step-by-step explanation:

sorey if i hav bad engelish im bad engelish

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".