Question 1201529
<font color=black size=3>
Answer: <font color=red size=4>12 pizzas</font>


====================================================================================


Work Shown:



p = number of pizzas the boys got
2p = number of pizzas the girls got
p+2p = 3p = total number of pizzas purchased
The goal is to find p, so we can calculate 3p.


x = number of boys = number of girls


x number of boys
1 boy eats 1/6 of a pizza
x boys eat x/6 of a pizza
Example: x = 36 boys eat x/6 = 36/6 = 6 pizzas


The boys got p number of pizzas
The boys ate x/6 number of pizzas.
They ate all of those pizzas, so p and x/6 must be the same.
p = x/6
6p = x
x = 6p
The number of boys is equal to 6 times the number of pizzas.
The same can be said about the number of girls.


x number of girls
1 girl eats 1/18 of a pizza
x girls eat x/18 = 6p/18 = p/3 of a pizza


2p = number of pizzas the girls got
p/3 = number of pizzas the girls ate
2p - p/3 = 6p/3 - p/3 = 5p/3 = number of pizzas left for the girls


Set that equal to the mixed number 6 & 2/3, aka the improper fraction 20/3, and solve for p.
5p/3 = 6 & 2/3
5p/3 = 20/3
5p = 20
p = 20/5
p = 4


The boys got 4 pizzas and the girls got 4*2 = 8 pizzas.
Total = 4+8 = <font color=red size=4>12 pizzas</font>
(or you could say 3p = 3*4 = <font color=red>12</font>)

--------------------------


Check:


p = 4 leads to x = 6*p = 6*4 = 24 boys and 24 girls (48 pupils total)


1 boy eats 1/6 of a pizza, so 24 boys eat 24/6 = 4 pizzas. This matches with p = 4, meaning the boys ate all of their allotted pizza.


1 girl eats 1/18 of a pizza, so 24 girls eat 24/18 = 4/3 = 1 & 1/3 pizza (i.e. 1 whole pizza plus another 1/3 of a pizza).
The girls got 2p = 2*4 = 8 pizzas.
Subtract off the amount they ate
8 - 4/3 = 8(3/3) - 4/3
8 - 4/3 = 24/3 - 4/3
8 - 4/3 = (24 - 4)/3
8 - 4/3 = 20/3
8 - 4/3 = (18+2)/3
8 - 4/3 = (18/3)+(2/3)
8 - 4/3 = 6+(2/3)
8 - 4/3 = 6 & 2/3
There are 6 whole pizzas, plus another 2/3 of a pizza, remaining for the girls. 
The answer has been confirmed.


There is probably a more efficient route, so feel free to explore alternatives.
</font>