Latoya Deshaun and Henry served a total of 90 orders Monday at the school cafeteria. Henry served 3 times as many orders as Deshaun. Latoya served 5 fewer orders than Deshaun. How many orders did they each serve?
Let's start by setting up equations for each person:
Henry = 3Deshaun
Latoya = Deshaun - 5
We also know that their total orders for the day was 90:
Henry + Deshaun + Latoya = 90
Now we can substitute the first two equations into the third equation:
3Deshaun + Deshaun + (Deshaun - 5) = 90
Combining like terms:
5Deshaun - 5 = 90
Adding 5 to both sides:
5Deshaun = 95
Dividing by 5:
Deshaun = 19
Now we can use the first two equations to find Henry's and Latoya's orders:
Henry = 3Deshaun = 3(19) = 57
Latoya = Deshaun - 5 = 19 - 5 = 14
Therefore, Deshaun served 19 orders, Henry served 57 orders, and Latoya served 14 orders on Monday.
Let's break this down step by step.
Let's assume that Deshaun served X orders.
Henry served 3 times as many orders as Deshaun, so he served 3X orders.
Latoya served 5 fewer orders than Deshaun, so she served (X - 5) orders.
Together, they served a total of 90 orders, so we can create the equation:
X + 3X + (X - 5) = 90
Combining like terms, we get:
5X - 5 = 90
Adding 5 to both sides, we have:
5X = 95
Dividing both sides by 5, we get:
X = 19
So, Deshaun served 19 orders, Henry served 3 times as many, or 3 * 19 = 57 orders, and Latoya served 5 fewer, or 19 - 5 = 14 orders.
Therefore, Deshaun served 19 orders, Henry served 57 orders, and Latoya served 14 orders.