4-7 Weighted Averages

•Mixture Problems•2 types

•Distance Problems

Suppose the Central Perk coffee shop sells a cup of espresso for $2.00 and a cup of cappuccino for $2.50. On Friday, Rachel sold 30 more cups of cappuccino than espresso, and she sold $178.50 worth of espresso and cappuccino. How many cups of each were sold?

Example #1: Mixture Problem Type 1

Item Amount Sold

Cost Total Cost

Espresso

Capp.

Concert Receipts: For a jazz concert, student tickets are $2 each and adult tickets are $4 each. If 200 tickets are sold and the receipts are $750, how many student tickets were sold?Item Amount

SoldCost Total Cost

Student

adult

Example #2: Mixture Problem Type 1

Mixing Candies: The owner of a store wants to make a 30 lb. mixture of two candies to sell for $3.00 per lb. If one candy sells for $2.95 per lb. and the other for 3.10 per lb., how many pounds of each should be used?

Item Amount Sold

Cost Total Cost

Candy 1

Candy 2

MIXTURE

The Quik Mart has two kinds of nuts. Pecans sell for $1.55 per pound and walnuts sell for $1.95 per pound. How many pounds of walnuts must be added to 15 pounds of pecans to make a mixture that sells for $1.75 per pound?Item Amount

SoldCost Total Cost

Pecans

Walnuts

MIXTURE

Example #4: Mixture Problem Type 2

OPPOSITE DIRECTIONS: 2 vehicles traveling in opposite directions – when will they meet?

One car leaves Chicago headed for Cleveland, a distance of 343 miles. At the same time, a 2nd car leaves Cleveland headed toward Chicago. If the 1st car averages 50 mph, and the 2nd car averages 48 mph, how long will it take for the cars to meet?Vehicle Rate Time Distance

Car 1

Car 2

HINT!! Distance of car 1 + Distance of car 2 = TOTAL DISTANCE

Example #5: Distance Problem

OVERTAKE PROBLEM: two vehicles traveling in SAME DIRECTION – when will one overtake the other?

A cyclist leaves Las Vegas riding at the rate of 18 mph. 1 hour later, a car leaves Vegas going 45 mph in the same direction. How long will it take the car to overtake the cyclist?Vehicle Rate Time Distance

Cyclist

Car

HINT!! Distance of car 1 = Distance of car 2

Example #6: Distance Problem

4-7 Homework