Objective – Understand Applications of Linear Systems Types of Problems 1)Number and Value Problems 2)Coin Problems 3)Mixture 4)Break-Even 5)Comparison 6)Boat or plane (current)

Number and Value Problem #1 -- Elimination John bought 15 items for $135. If the 15 items consisted of notebooks that cost $4.50 each and calculators that cost $12.00 each, how many of each did he buy? Let x = # of notebooksLet y = # of calculators

Number and Value Problem #1 -- Substitution David bought 15 items for $135. If the 15 items consisted of notebooks that cost $4.50 each and calculators that cost $12.00 each, how many of each did he buy? Let x = # of notebooksLet y = # of calculators

Number and Value Problem #2 Willa raised $24 by selling 40 baked items for the PTA. She sold cookies for 50 cents each and brownies for 75 cents each. How many of each did she sell? Let c = # of cookiesLet b = # of brownies

World Famous Coin Problem Elly had 400 coins worth $25. She only had nickels and dimes. How many of each did she have? Let n = nickelsLet d = dimes

World Famous Coin Problem – YOU DO!! Emma had 140 coins worth $23. She only had quarters and dimes. How many of each did she have? Let q = quartersLet d = dimes

Mixture Problem #1 A 12 pound mixture of peanuts and cashews sells for $6.50/lb. If peanuts sell for $3 per pound and cashews sell for $8 per pound, how many pounds of peanuts are in the mix? Let p = peanuts (in lbs.)Let c = cashews(in lbs.)

Mixture Problem #2 A 10% acid solution is mixed with a 60% acid solution to produce 120 liters of a solution that is 40% acid. How much of each solution was used to create the mixture? Let x = liters of 10% sol. Let y = liters of 60% sol.

Comparison Problem The population of Bentville is 50,000 but is growing at 2500 people per year. Payton Valley has a population of 26,000 but is growing at 4000 people per year. When will both towns have equal population. Let x = # of yearsLet p = population BentvillePaytonValley

Breakeven Problem Sam is starting a candied yam business. Sam buys each yam for $1.25 and spend $5000 on wages and $2500 on Utilities. If Sam sells each candied yam for $4, how many yams will Sam need to sell to Breakeven? Keys to Breakeven Problems Not Really a System (if you combine the problem) Set Up 1 Big Equation Equal to 0 (breakeven) Be Aware of Good Things (money made) and Bad Things (Money Spent) 4x – 1.25x – 5000 – 2500 = 0 Solve for X !!!

Boat (current or jetstream) Problem Passi and a friend take 3.2 hrs to canoe downstream 12 miles. Going back upstream took 4.8 hrs. If they paddled at the same rate, what was their speed in still water and the current’s speed? Key to Motion Problems – Use an RTD Table (and divide by time to simplify)

Plane (jetstream) Problem Laura and a friend flew 7 hrs to go 2800 miles from Miami to Seattle. The return trip took 5.6hrs. If The airspeed was the same, what was the jetstream? Key to Motion Problems – Use an RTD Table (then Divide by time to simplify) x = 450 and y =50