Final answer:
To solve this problem, you can assign variables to each person's number of orders and create a system of equations. By solving the system, you can find the values of each person's orders.
Step-by-step explanation:
To solve this problem, let's assign variables to each person's number of orders. Let's say Nicole served x orders, Goran served y orders, and Henry served z orders.
We are given that Nicole served more orders than Goran, so we have the inequality x > y. We are also given that Henry served 3 times as many orders as Goran, so we have the equation z = 3y.
Since Nicole, Goran, and Henry served a total of b orders, we have the equation x + y + z = b. Now we can substitute z = 3y into the equation and solve for x and y.
Substituting z = 3y into the equation x + y + z = b, we get x + y + 3y = b. Simplifying this equation, we have x + 4y = b. We also know that x > y, so we can say that x = y + c, where c is a positive constant.
Substituting x = y + c into the equation x + 4y = b, we get y + c + 4y = b. Combining like terms, we have 5y + c = b. Now we have two equations: x = y + c and 5y + c = b.
Since we are trying to find the number of orders each person served, we need to find the values of x, y, and z. To do this, we need another equation relating x, y, and z. We know that Henry served 3 times as many orders as Goran, so we can say that z = 3y. Now we can substitute this into the equation x + y + z = b, giving us x + y + 3y = b. Simplifying, we have x + 4y = b.
Now we have the system of equations: x = y + c, 5y + c = b, and x + 4y = b. From this system, we can solve for the values of x, y, and z.
Let's say b represents the total number of orders served by Nicole, Goran, and Henry. By solving the system of equations, we can find the values of each person's orders:
- Nicole: x
- Goran: y
- Henry: z
Therefore, Nicole served x orders, Goran served y orders, and Henry served z orders.