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1 Math 154A Chapter 5.4: Solving Application Problems Part 1 Objectives: Ticket and cookie sales Finding single price of multiple items Finding when two options cost the same Interest problems Mixture problems Ticket and Cookie Sales Chapter 5.4 (Part1) Steps for Solving Application Problems: 1. Read, throw out nonsense numbers 2. Assign a variable (What is it asking for?) 3. Write an equation 4. Solve the equation 5. Answer the question! 6. Check, does it make sense? Ex: Say a movie theater charges $5 for children and $11 for adults. One night a group of 41 people spent $307 on tickets. How many adult tickets were sold and how many children tickets were sold? number of children tickets money made from child tickets number of adult tickets money made from adult tickets totalnumber of tickets totalmoney made Answers: 24 = number of child tickets sold 17 = number of adult tickets sold 1. You decided to have a bake sale, where you sold 100 cupcakes and cookies. The cupcakes sold for $5 each and the cookies sold for $4.75 each. Find the number of cupcakes and cookies that were sold if the total income from the bake sale was $490. number of cupcakessold money made from cupcakesales number of cookiessold money made from cookiesales totalsold totalmoney made Answers: 60 = number of cupcakes sold 40 = number of cookies sold

2 2. A coin purse contains a mixture of 49 coins in quarters and dimes. The coins have a total value of $8.95. Determine the number of quarters and number of dimes in the coin purse. number of quarters (0.25)(number of quarters) number of dimes totalnumber of coins (0.10)(number of dimes) totalmoney Answers: 27 = number of quarters 22 = number of dimes Finding Single Price of Multiple Items Ex: At a professional football game, the cost of 2 bottles of water and 3 pretzels is $ The cost of 4 bottles of water and 1 pretzel is $ Determine the cost of a bottle of water and the cost of a pretzel. Answers: $3 = cost of one water bottle $3.50 = cost of one pretzel

3 1. The other day I went to Staples to buy some office supplies. I bought 5 pens and 2 binders, which together cost me $ My friend bought 3 of the same pens and 4 of the same binders, and it cost her $ What are the cost for a single pen and the cost for a single binder? Answers: $1.25 = cost of one pen $3.50 = cost of one binder 2. One fan at a rock concert bought 2 long-sleeve shirts and 3 short-sleeve shirts for a total of $68. Another fan bought 4 long-sleeve shirts and 2 short-sleeve shirts for $88. How much does one longsleeve shirt cost and how much does one short-sleeve shirt cost? Answers: $16 = cost of one long-sleeve shirt $12 = cost of one short-sleeve shirt

4 Finding When Two Options Cost the Same Ex: Sales position A pays $250 a week plus a 5% commission (a percentage of the sales you made for the company by selling widgets). Sales position B pays $300 a week plus a 4% commission. Let = Then = Salary A, and = Salary B a) Find the amount of money from widget sales per week that would be necessary for both positions to pay the same. Equation: Salary A Salary B b) If you plan to make the company $6,000 per week in widget sales, which position pays better? Answer: a) $5000 = widget sales for both salaries to pay the same b) Salary A = $550 (better choice) 1. Car Rental Company A charges $50 per day plus $.18 per mile. Car Rental Company B charges $64 per day plus $.11 per mile. Let = _ Then _= Company A plan, and = Company B plan a) Find the number of miles that must be driven that day for both companies to cost the same. Equation: Company A plan Company B plan b) Say you were planning on driving 150 miles that day, which rental company should you use? Answer: a) 200 miles = for both companies to cost the same b) Company A = $77 (cheaper choice)

5 Interest Problems Formula for 1 year: Interest = (principal)x(rate) Ex: Say you invested $8,000 into two accounts. The first account has an 11% interest rate and the second account has a 12% interest rate. How much do you have invested in each account if the total interest gained on both accounts in one year was $940? Let = _ Let = _ money investedin 11%account interest gainedfrom11%account money investedin 12%account interest gainedfrom12%account totalmoney invested totalinterest gained Answer: $2,000 = amount invested at 11% interest $6,000 = amount invested at 12% interest 1. Say you invested $13,400 into two accounts. The first account has a 3% interest rate and the second account has a 4% interest rate. How much do you have invested in each account if the total interest gained on both accounts in one year was $466? Let = _ Let = _ money investedin 3%account interest gainedfrom 3%account money investedin 4%account interest gainedfrom 4%account totalmoney invested totalinterest gained Answer: $7,000 = amount invested at 3% interest $6,400 = amount invested at 4% interest

6 Mixture Problems Ex: How many liters of 40% solution and 65% solution must be added to obtain 50 liters of 60% solution? Let = _ Let = # of liters of 40% _ (0.4)(#of liters of 40%solution) # of liters of 65% _ total# of liters of solution (0.65)(#of liters of 65%solution) _ (0.6)(#of liters of mixture) Answer: 10 = liters of 40% solution 40 = liters of 65% solution 1. How many liters of 15% solution and 40% solution must be added to obtain 10 liters of 20% solution? Let = _ Let = # of liters of15% _ (0.15)(#of liters of15%solution) # of liters of 40% _ (0.4)(#of liters of 40%solution) total# of liters of solution _ (0.2)(#of liters of mixture) Answer: 8 = liters of 15% solution 2 = liters of 40% solution