Please, see the attached graph.
1) All 3 vegetarians in the Troop wanted mushrooms only. In the graph mushrooms only is "a", then a=3.
2) 1 person wanted all 3 toppings. In the graph, all 3 toppings is "c", then c=1.
3) 2 wanted chicken and pepperoni only. In the graph, chicken and pepperoni only is "f", then f=2.
4) 2 wanted pepperoni and mushroom only. In the graph, pepperoni and mushroom only is "d", then d=2.
5) 10 requested toppings that included pepperoni. In the graph, pepperoni is "c+d+f+g", then:
c+d+f+g=10
c=1, d=2, f=2. Replacing the values in the equation above:
1+2+2+g=10
Adding the numbers:
5+g=10
Solving for g:
5+g-5=10-5
g=5
6) 9 requested toppings that included mushroom. In the graph, mushroom is "a+b+c+d", then:
a+b+c+d=9
a=3, c=1, d=2. Replacing the values in the equation above:
3+b+1+2=9
Adding the numbers:
b+6=9
Solving for b:
b+6-6=9-6
b=3
7) 12 people requested toppings that included chicken. In the graph, chicken is "b+c+e+f", then:
b+c+e+f=12
b=3, c=1, f=2. Replacing the values in the equation above:
3+1+e+2=12
Adding the numbers:
e+6=12
Solving for e:
e+6-6=12-6
e=6
8) There were 32 people altogether. In the graph, the total is "a+b+c+d+e+f+g+h", then:
a+b+c+d+e+f+g+h=32
a=3, b=3, c=1, d=2, e=6, f=2, g=5. Replacing the values in the equation above:
3+3+1+2+6+2+5+h=32
Adding the numbers:
h+22=32
Solving for h:
h+22-22=32-22
h=10
Answer: The final order that Chris placed at Pizza Shack was:
a) 10 plain
2) 3 mushrooms only
3) 6 chichen only
4) 5 pepperoni only
5) 2 chicken and pepperoni only
6) 2 peperoni and mushrooms only
7) 3 mushrooms and chicken only
8) 1 with all 3 toppings
