SOLUTION: Mr Cody bought some pizzas for a group of pupils. There was an equal number of girls and boys. The girls received 2 times as many pizzas as the boys. Each boy ate 1/6 of a pizza an

Question 1201529: Mr Cody bought some pizzas for a group of pupils. There was an equal number of girls and boys. The girls received 2 times as many pizzas as the boys. Each boy ate 1/6 of a pizza and the boys finished all the pizzas given to them. Each girl ate 1/18 of a pizza and the girls had 6 2/3 pizzas left. How many pizzas did Mr Cody buy?
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: 12 pizzas

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

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 = 12 pizzas
(or you could say 3p = 3*4 = 12)
--------------------------

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.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let x be the number of boys and the number of girls.

The boys each ate 1/6 of a pizza; the number of pizzas the boys ate was x(1/6) = x/6. They ate all the pizzas they got, so the number of pizzas they got was x/6.

The girls each ate 1/18 of a pizza; the number of pizzas they ate was x(1/18) = x/18. They finished with 6 2/3 pizzas left over. The number of pizzas they got was x/18 + 6 2/3 = x/18 + 20/3.

The number of pizzas the girls got was twice the number the boys got:

x/18 + 20/3 = 2(x/6)

Multiply by 18 to clear fractions....

x+120 = 6x
5x = 120
x = 24

There were 24 boys and 24 girls in the group.

Each of the 24 boys ate 1/6 of a pizza; that makes 4 pizzas.

The girls got twice as many pizzas as the boys, so the girls got 8 pizzas.

So the total number of pizzas Mr. Cody bought was 4+8 = 12.

ANSWER: 12

RELATED QUESTIONS
There were 44 boys and 47 girls in a camp. The boys and girls were divided into groups.... (answered by JulietG)
There was an equal number of boys and girls in a school auditorium. After 24 boys left... (answered by math_helper)
From a group of boys and girls, 14 girls leave first. Then the ratio of the number of... (answered by richwmiller)
From a group of boys and girls, 14 girls leave first. Then the ratio of the number of... (answered by ankor@dixie-net.com)
From an original group of boys and girls, twenty girls leave. There are then left two... (answered by josmiceli)
An equal number of boys and girls attended a birthday party. When 16 girls left, there... (answered by stanbon,josmiceli)
Hi The number of boys was 5 times the number of girls at first. When an equal number of... (answered by josgarithmetic)
The number of girls in Mr Beckers Algebra class exceeded the number of boys by 4. If... (answered by jojo14344)
A six-person committee must be formed from a group of 6 boys and 7 girls. a) Determine... (answered by Boreal)