One remote is defective for every 199 non-defective remotes.

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 .

To begin, you need to calculate how many students are taking Old Norse. This is:

Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:

Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of :

This is the same as .

To begin, you need to do a simple addition to find the total number of flowers in the garden:

Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by . This is:

Next, reduce the fraction by dividing out the common  from the numerator and the denominator:

This is the same as .

Max will be X in 5 years. So today he is X -5 and 4 years ago he was (X-5)  - 4, that is X – 9.  It always helps to put numbers into the equations. Example: Max will be 12 in 5 years. How old was he 4 years ago? So today Max is 12 – 5 = 7.  Therefore, four years ago he was 7 -4 =3. Which is 12-5-4 =12-9 = 3

It is $12 divided by 8 which is $1.50. The number of slices in the pizza pie is not relevant in this question.

 We first find out how much each person must run.  Thus we take 110/5 to get 22 yards.  However, Jim must run twice the amount of a normal competitor, so we multiply by 2 to get 44 yards.

This problem can be set up as a proportion: 30 feet/x feet = 50 feet/100 feet. To solve, we simply cross multiply: (30 feet * 100 feet) = (50 feet * x feet). Thus, 3000 feet = 50x feet. To solve for x, divide each side by 50. Therefore, x = 60 feet.  If you got 167 feet, you may have set up the proportion incorrectly by mixing up the height of the building with the length of the shadow. If you got 6 feet or 600 feet, you may have made a computational error. If you got 1670 feet, you may have set the proportion up incorrectly and made a computational error.

0.8 mile.  Using some conversions:  ( (24mi/1hr)*(1hr/60min)*2min = 0.8 mile

25,500 lbs of concrete. Setting up a ratio with x representing the number of pounds concrete the 3,000 of cement produces, we obtain the relation: (10,000/85,000) = (3,000/x), x = 25,500 pounds of concrete.