Since the problem is focusing on Carol, we will only worry about Carol's contribution to the bill.

The original split on the bill was with Carol paying the smaller portion. With parts, each one was . This was originally the amount Carol was responsible for.

With the the ratio of , this meant there are parts with each being . Carol pays instead .

The difference is then or .

If Jill, Jack and John get , that means there are parts.

Because they found , each part gets or .

Jack gets or .

John gets or .

Since the question is asking how much more did Jack get than John, we subtract and to get .

If there are girls and boys, that means we have students in the class. To continue to have this ratio, we need an answer than is a multiple of .

is a multiple of which is the right answer.

27 of the 72 cars are 4-wheel drive, we can write this as a proportion.

The proportion of the 4-wheel drive cars to the total number of vehicles.

Therefore, to find the proportion of 2-wheel drive cars is,

Therefore the ratio of 2-wheel drive:4-wheel drive vehicles is 5:3.

You don't need to solve for the actual number of broken or unbroken dolls. Instead, put the percentages in the ratio because no matter what, the percentages are fixed regardless of amount of dolls broken or unbroken.

So the question is asking for broken to unbroken. The percentage of broken dolls is .

So we have a ratio of or .

First, compute the new number of philosophy books. This will be .

The ratio of philosophy books to history books is thus:

This can be reduced by dividing the numerator and the denominator by :

Therefore, the ratio is .

Begin by making your life easier: presume that there are papers on the desk. Immediately, we know that there are paper clips. Now, if there are papers, you know that there also must be greeting cards. Technically you figure this out by using the ratio:

By cross-multiplying you get:

Solving for , you clearly get .

(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)

Now, this means that our desk has on it:

papers

paper clips

greeting cards

Therefore, you have total items. Based on this, your ratio of paper clips to total items is:

, which is the same as .

Let's convert the words into numbers. Since there are girls and boys, we need ratio of boys to girls. The ratio should be .

To find an integer ratio, let's find the fractions with a common denominator. This will be . Then, we multiply the left by and the right by to get fractions of and . With the same denominators, we just have numerators to compare. Ratio is then .

A ratio is two numbers separated by a colon. When expressing fractions as a ratio, the numerator is the number to the left of the colon while the denominator is to the right of the colon. The answer is