Jessica, Kareem, and Lamar served a total of 64 orders Monday at the school cafeteria. Jessica served 8 fewer orders than Lamar. Kareem served 2 times as many orders as Lamar. How many orders did they each serve?

Jessica: 10 orders

Lamar: 18 orders

Kareem: 36 orders

Step-by-step explanation:

Let's first designate each person with a letter.

The number of orders served by Jessica can be designated as

The number of orders served by Kareem can be designated as

The number of orders served by Lamar can be designated as

We know that they all served a total of 64 orders. This can be expressed as the sum of their orders equaling 64.

We also know that Jessica served 8 fewer orders than Lamar. This can be expressed as the number of orders served by Jessica, , being equal to Lamar's orders minus 8.

Fianlly, we know that Kareem served twice as many orders as Lamar. This can be expressed as the number of order's served by Kareem, , being 2 times Lamar's orders .

With these 2 equalities, we can substitute and in our original equation,

with their values expressed as a subtraction or multiplication of .

will be substituted with , and will be substituted with .

With substitutions:

We can simplify this by combining the L-terms:

Next, we'll add 8 to both sides.

Divide both sides by 4:

Thus, Lamar served 18 orders.

Using our expressions, we can find how many orders the others served.

Jessica:

Jessica served 10 orders.

Kareem:

Kareem served 36 orders.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0