2-9 Weighted Averages Mixture Problems Percent Mixture Problem Speed of One Vehicle Speed of Two Vehicles

A Quick Review 6r + t = r-1 Solve for r. 4c – d = 4a – 2c Solve for c 7𝑔+ℎ 𝑏 = -2 solve for h Use the formula A= 1 2 (a+ b ) to find the height of the trapezoid if a= 8 cm and b = 17 cm.

A Quick Review On a map, the distance between two cities measures 6 3 10 inches. The scale of the map is ½ inch = 75 miles. What is the actual distance between the two cities? EQ: Why is it important to be able to express mathematical expressions in different ways. Activities for today: Warm-up Questions on homework Review Review vocabulary words from 2-8 Notes from 2-9 Classwork/Homework You will be able to… Solve mixture problems Solve uniform motion problems

Weighted Averages New vocabulary Weighted average Mixture problem Uniform motion problem Rate problem Madisha feeds her cat gourmet cat food that costs $1.75 She combines it with cheaper food that costs $0.50 per pound. How many pounds of cheaper food should Mandisha buy to go with 5 pounds of gourmet food, if she wants the average price to be $1.00 per pound? Units (lb) Price per Unit Total Price Gourmet cat food Cheap cat food Mixed cat food

More examples A car’s radiator should contain a solution of 50% antifreeze. Bae has 2 gallons of a 35% antifreeze. How many gallons of 100% antifreeze should Bae add to his solution to produce a solution of 50%? Let g = the number of gallons of 100% antifreeze to be added. Fill in the table. Amt of Solution (gal) Amt of Antifreeze 35% solution 100% solution 50% solution

Real World Examples 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? r t d=rt Fast Train Other train

Real World Examples Cheryl bought 3 ounces of glass beads that cost $1.79 an ounce. The seed beads cost $.99 an ounce. How many ounces of seed beads can she buy if she only wants the beads to be $1.29 an ounce for her craft project? Units (lb) Price per Unit Total Price Glass beads Seed Project beads

Real World Examples A recipe calls for mixed nuts with 50% peanuts. 1 2 pound of 15% peanuts has already been used. How many pounds of 75% peanuts needs to be added to obtain the required 50% mix?

Real world examples Two students left the school on their bicycles at the same time, one heading north and the other heading south. The student heading north travels 15 miles per hour, and the one heading south travels at 17 miles per hour. After about how many minutes will they be 7.5 miles apart?

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