Manjeet made a pizza for his family using their four favorite toppings - pepperoni, mushrooms, onions and olives. He put twice as many onions as pepperoni and half as many mushrooms as olives. If there are 39 individual toppings on the pizza how many of each topping did he use? How many different combinations can you come up with?

Let

x = the number of pepperoni added to the pizza.

y = the number of mushrooms added to the pizza.

z = the number of onions added to the pizza.

u = the number of olives added to the pizza.

Twice as many onions as pepperoni

z = 2*x

Half as many mushrooms as olives

y = u/2

There are 39 individual toppings on the pizza

x + y + z + u = 39

We are dealing with a system of equation with 4 unknowns and only three equations.

2*x - z = 0

y - u/2 = 0

x + y + z + u = 39

This means that there are an infinite number of solutions for your problem

For example, here is one solution

x = 1

z = 2

1 + y + 2 + (2y) = 39

3y = 36

y = 12

u = 24