- Solve mixture problems
- Solve uniform motion problems
Sometimes the numbers that go into an average do not all have the same weight or importance. In such cases, you may want to use a weighted average.
Weighed Average = value(unit) + value(unit) +.../number of units
Two applications of weighted averages are:
- mixture problems and
- problems involving uniform motion, or motion at a constant rate or speed.
Example 1: Solve a Mixture Problem with Price
Jeri likes to feed her cat gourmet cat food that costs $1.75 per pound. However, food at that price is too expensive so she combines it with cheaper cat food that costs $0.50 per pound. How many pounds of cheaper food should Jeri buy to go with 5 pounds of gourmet food, if she wants the price to be $1.00 per pound?
NOTE: Use the 4 step plan
1.) Explore- write down given and identify what your asked to find
2.) Plan- define variable
3.) Solve - Make a table with useful information. Put units on top and what your look for on the side
4.) Examine- check your answer in the context of the original problem.
Solution
Example 2: Solve a Mixture Problem with Percents
Example 3: Solve for Average Speed
On Alberto's drive to his aunt's house, the traffic was light, and he drove the 45-mile trip in one hour. However, the return trip took him two hours. What was hi average speed for the round trip?
Solution
To find the average speed for each leg of the trip use d = rt and solve for r.
Going: r = d/t, r = 24/1 = 45 miles per hour
Returning: r = d/t, r = 24/2 = 22.5 miles per hour
Note: You know must find the weighted average for the trip.
Use the weighted average M,
M = 45(1) + 22.5(2)/1 + 2 = 90/ 3 = 30
Therefore, Alberto's average speed was 30 miles per hour
