Question:  Ellie loves to count and keep track of data as much as she loves roller coasters. Naturally, while at the theme park for her birthday, Ellie counted the rides. Of the rides she counted, she discovered that 1/2 were regular roller coaster rides. One-eighth of the rides were built for children and 1/4 were water rides. Finally, Ellie counted 4 special coasters that went upside down or were hanging rides. How many roller coasters did Ellie count of each ride and how many were there altogether?

Answer:  This problem can be solved by working backwards to find the total (one whole) and then determine how many of each using the fractional clues.

1. Since you know that 4 were special coasters, you need to find out what fraction of the total this is.

2. Add the other fractions up.

3. Since all the other coasters are 7/8 of the total, the 4 special coasters must be 1/8, or. . .

4. We knew that 1/8 is also the number of children's rides so there must also be 4 of those.

5. ¼ of the rides (or 2/8) were water rides. If 4 represents 1/8 then 8 must represent ¼.

6. Finally, ½ of the rides are regular rides. If 4 coasters are 1/8 of the total, and 8 rides are ¼ of the total, then 16 must be ½ of the total. So, there must be 16 regular coasters.