If  ounces fills the pitcher, then it must equal the volume of  of the pitcher.  If  of a pitcher equals 27 ounces, then  of a pitcher equals ounces.  Since there are  fifths in the pitcher, it must hold  ounces total.

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class:

8 = (1/3) x, where x is the number in the entire class.

When we solve for x in the equation we get x = 24.

With the given information, we can set up a proportion. 

Multiply both the numerators or denominators by 100 to eliminate the decimals

Simplify both fractions

Multiply the numerators and multiply the denominators and simplify the fraction by dividing both the numerator and denominator by 5.

Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively.  Therefore, the only answer which is within the desired range is 2/5.

The greatest common divisor is 4. This means that both numbers must be divisible by 4.  Furthermore, the least common multiple is 40, so both must divide 40.

The prime factorization of 40 is .  For a number to divide 40, it must therefore be composed of (at most) three 2's and one 5.  Because  divides both numbers, we also know that they must both have at least two 2's.

Now each number will have either two or three 2's and zero or one 5's.  However, we also know that they can't both have three 2's, (since then the greatest common divisor would have three 2's as well).  Similarly, only one can have a 5. 

In essence, our problem becomes one of choice.  We have 2 places with value 4.  We choose to give a 5 to one of the two. We then give a 2 to one of the two. If we give a 5 and a 2 to the same side, we end up with  and 4. If we give a 5 to one and a 2 to the other, we end up with  and .

Thus our two pairs are:

4,40 and 8,20

To add fractions you must first find the lease common denominator, that is, a number that all of the denominators (the bottom number) can divide into.

In this case, 5, 3, and 30, both 5 and 3 divide successfully into 30, so 30 is the least common denominator. 

Now divide each smaller denominator into thirty.  Then multiple the answer by the top number:

5/30 = 6

Therefore 4/5 = 4*6 / 5*6 = 24/30

3/30 = 10

Therefore 7*10 / 3*10 = 70/30

Then add all the numerators together:

24/30 + 70/30 +9/30 = (24+70+9)/30 = 103 / 30

For this problem it would be easier to choose one of the answers and go from there. 108 works because 1/4 of 108 is 27 then 2/3 of 27 is 18 and 1/18 of 18 is 1, which makes this answer possible.

The other answers come out with a remainders that make no sense, since a fractional part of a person cannot have been accepted to a school.

Rewrite each fraction into an improper fraction.

The common denominator is 16.

The correct answer is:  

 becomes