Question

Chris visited the local Pizza Shack to purchase one pizza for each member of his Scout Troop. On arrival, he realised that he had mislaid the list he had made of the pizzas that had been requested. He knew that there were 32 people altogether and that all 3 vegetarians in the Troop wanted mushrooms only. He also remembered that the same number of people wanted just the chicken topping as wanted a plain pizza. Alex, a Young Leader, was able to help by recalling that: 12 people requested toppings that included chicken, 10 requested toppings that included pepperoni, 9 requested toppings that included mushroom, 1 person wanted all 3 toppings, 2 wanted chicken and pepperoni only, 2 wanted peperoni and mushroom only. What was the final order that Chris placed at Pizza Shack?

Answer 1

Look at the attached

Answer 2

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