Math 141-copyright Joe Kahlig, 10A Page 1Section 2.1: Systems of Linear EquationsExample: Set up the following word p roblems. Do not solve (yet). Be sure that the variables aredefined.1. You own a hamburger stand and your current inventory includes 86 bread rolls, 100 beef pat-ties, and 140 cheese slices. Your menu consists of three types of h amburgers: plain, doublecheeseburger, and regular cheeseburger. Each plain hamburger require 1 beef patty and 1 breadroll. Each double cheeseburger requires 1 bread roll, 2 beef patties, and 4 cheese slices. Eachregular cheese burger requires 2 cheese slices, 1 bread r oll, and 1 beef patty. How many of eachhamburger should you make so that all resources are used?2. The city of Aurora gets a matching grant of $1 million ( making a total of $2 million) to spendin these categories: streets, sewers, and parks. The city council decides that the amount spenton parks should equal the total amount spent on streets and sewers and that, furthermore, twiceas much should be spent on parks as on sewers. How much money is to allotted to each of thesecategories?3. Link has $7,000 to invest. He decides to invest in three different companies. The Q X companycosts $25 per share and pays dividends of $0.75 per share each year. The RY company costs $40per share and p ay dividends of $1.50 per share each year. The KZ company costs $15 per shareand pays $2.00 per share per year in dividends. Link wants to have twice as much money in theRY company as in the KZ company. Link also wants to earn $352 in dividends per year. Howmuch should Link invest in each company to meet his goals?Math 141-copyright Joe Kahlig, 10A Page 24. Link has $7,000 to invest. He decides to invest in three different companies. The QX companycosts $25 per share and pays dividends of $0.75 per share each year. The RY company costs $40per share and p ay dividends of $1.50 per share each year. The KZ company costs $15 per shareand pays $2.00 per share per year in dividends. Link wants to have twice as much money in theRY company as in the KZ company. Link also wants to earn $352 in dividends per year. Howmuch should Link invest in each company to meet his goals?5. A brokerage firm packaged blocks of blue-chip stocks, bonds and high-risk stocks into threeportfolios, which it offers to its cu s tomers. The makeup of each portfolio is given in the table. Acustomer wants eight blocks of blue-chip stocks, 11 blocks of bon ds, and nine blocks of high-riskstocks. How many of each portfolio should the customer purchase?Portfolioblue chip stocks bonds high-risk stocksI 1 block 4 blocks 3 blocksII 2 blocks 1 block 2 blocksIII 4 blocks 2 blocks 1
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