Question

"You rent four movies and return them a day late. The regular rental fee is xdollars per movie. You are charged a total of (4x+8) dollars. a. Factor the expression using the cake method (GCF).(4x+8) = __________ Don't put spaces when you type your answer. b. The fee for returning a movie 1 day late is $__________"

Answer 1

a. 4(x + 2)

b. $2.00

Explanation:

The 'cake method' is another method that can be used to find greatest common factor (GCF) and least common multiple (LCM). In this method, you form an 'upside down layered cake' to factor your numbers:

Start with your two numbers: 4 8

Look at what two factors you can multiply to find those numbers and put the common number on the outside and the other number down below:

2 I 4 8 I

2 I 2 4 I

1 I 1 2 I

Now, multiply the numbers on the left side of the cake (2 x 2 x 1), GCF = 4.

With the GCF = 4, put this number outside the parenthesis and factor: 4(x + 2). Since 'x' represents the cost of one movie rental, then the fee for returning a movie 1 day late is $2.00.

Answer 2

Explanation:

Let's call
`x` the amount of dollars per movie.

The following expression represents charges in dollars:
`4x+8`

If we use the cake method, it would be like the following:

| 4 8

2 | 2 4

2 | 1 2

So, the Greatest Common Factor is 2 times 2, which is 4. GCF = 4.

a. The factored expression would be:
`4(x+2)`

Notice that the charge per movie is $(x+2), because the factor 4 represents the total number of movies.

Therefore, in this case, the fee per movie is x + 2. (b).