Question

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?

Answer 1

Answer:

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 $J$

The number of orders served by Kareem can be designated as $K$

The number of orders served by Lamar can be designated as $L$

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

$J+K+L=64$

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

$J = L-8$

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, $K$, being 2 times Lamar's orders $L$.

$K = 2L$

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

$J+K+L=64$

with their values expressed as a subtraction or multiplication of $L$.

$J$ will be substituted with $L-8$, and $K$ will be substituted with $2L$.

$J+K+L=64$

With substitutions:

$(L-8) + 2L + L = 64$

We can simplify this by combining the L-terms:

$L + 2L + L -8 = 64\\4L - 8 = 64$

Next, we'll add 8 to both sides.

$4L = 72$

Divide both sides by 4:

$L = 18$

Thus, Lamar served 18 orders.

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

Jessica:

$J = L-8\\J = 18 -8\\J = 10$

Jessica served 10 orders.

Kareem:

$K = 2L\\K = 2*18\\K = 36$

Kareem served 36 orders.