2-9 Notes for Algebra 1 Weighted Averages

Weighted Averages Weighted average M of a set of data is found by multiplying each data value by its weight and then finding the mean of the new data set.

Mixture Problems Problems in which two or more parts are combined into a whole. They are solved using weighted averages.

Example 1 pg. 132 Real World Example PETS Mandy feeds her cat gourmet cat food that costs $1.75 per pound. She combines it with cheaper food that costs $0.50 per pound. How many pounds of cheaper food should Mandy buy to go with 5 pounds of gourmet food, if she wants the average price to be $1.00 per pound?

Example 1 pg. 132 Real World Example PETS Mandy feeds her cat gourmet cat food that costs $1.75 per pound. She combines it with cheaper food that costs $0.50 per pound. How many pounds of cheaper food should Mandy buy to go with 5 pounds of gourmet food, if she wants the average price to be $1.00 per pound? 7.5 lb. of cheaper food 1.75 5 +0.50 𝑥 =1.00 5+𝑥

Example 2 pg. 133 Real World Example AUTO MAINTENANCE A car’s radiator should contain a solution of 50% antifreeze. Bae has 2 gallons of 35% antifreeze. How many gallons of 100% antifreeze should he add to his solution to produce a solution of 50% antifreeze?

Example 2 pg. 133 Real World Example AUTO MAINTENANCE A car’s radiator should contain a solution of 50% antifreeze. Bae has 2 gallons of 35% antifreeze. How many gallons of 100% antifreeze should he add to his solution to produce a solution of 50% antifreeze? 0.6 gal of 100% antifreeze 35% 2 +100% 𝑥 =50% 2+𝑥

Uniform Motion Problems/Rate Problems Problems in which an object moves at a certain speed or rate. 𝑑=𝑟𝑡 is often used to help solve these problems. d-distance, r-rate, t-time.

Example 3 pg. 134 Real world Examples 1.) AIR TRAVEL Nita took a non-stop flight to visit her grandmother. The 750-mile trip took three hours and 45 minutes. Because of bad weather, the return trip took four hour and 45 minutes. What was her average speed for the round trip.

Example 3 pg. 134 Real world Examples 1.) AIR TRAVEL Nita took a non-stop flight to visit her grandmother. The 750-mile trip took three hours and 45 minutes. Because of bad weather, the return trip took four hours and 45 minutes. What was her average speed for the round trip. The average speed for the round trip was about 176 mph. 750 3 3 4 3 3 4 + 750 4 3 4 4 3 4 3 3 4 + 4 3 4

Example 4 pg. 135 Real world example 1.) RESCUE A railroad switching operator has discovered that two trains are heading toward each other on the same track. Currently, the trains are 53 miles apart. One train is traveling at 75 miles per hour and the other 40 miles per hour. The faster train will require 5 miles to stop safely, and the slower train will require 3 miles to stop safely. About how many minutes does the operator have to warn the train engineers to stop their trains

Example 4 pg. 135 Real world example 1.) RESCUE A railroad switching operator has discovered that two trains are heading toward each other on the same track. Currently, the trains are 53 miles apart. One train is traveling at 75 miles per hour and the other 40 miles per hour. The faster train will require 5 miles to stop safely, and the slower train will require 3 miles to stop safely. About how many minutes does the operator have to warn the train engineers to stop their trains? about 23 minutes 75𝑡+40𝑡=53 ; train A time to stop = 5 75 ; train B time to stop= 3 40 (𝑡−𝑙𝑜𝑛𝑔𝑒𝑠𝑡 𝑡𝑖𝑚𝑒 𝑡𝑜 𝑠𝑡𝑜𝑝 𝑖𝑛 ℎ𝑜𝑢𝑟𝑠) 60

2-9 pg. 136 7-13o, 15-45(x3)