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SYSTEMS OF EQUATIONS

SYSTEMS OF EQUATIONS. COIN AND MONEY PROBLEMS. WARM UP. Choose the best method to solve the system: 4s – 3t = 8 and t = -2s – 1.

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SYSTEMS OF EQUATIONS

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  1. SYSTEMS OF EQUATIONS COIN AND MONEY PROBLEMS

  2. WARM UP Choose the best method to solve the system: 4s – 3t = 8 and t = -2s – 1. Printing a newsletter costs $1.50 per copy plus $450 in printer’s fees. The copies are sold for $3 each. How many copies of the newsletter must be sold to break even? A rectangle has a perimeter of 34 cm and an area of 52 cm². Its length is five more than twice its width. Write and solve a system of equations to find the dimensions of the rectangle. Tell whether the system has one solution, infinitely many solutions, or no solutions. y = ½x + 3 and 2y – x = 6

  3. Lucy has a collection of dimes and quarters. If she has 80 coins in all and their total value is $12.20, how many coins are there of each type?

  4. Matt has twice as many quarters as dimes in his coin collection. If the dimes and quarter together total $9.00, how many of each kind of coin does he have?

  5. Cecelia bought some 22c and some 17c stamps for the school office. Altogether she purchased 37 stamps for $7.54. How many stamps of each kind did she buy?

  6. Bus fares from Amherst to Mount Mohawk are $26 for adults and $18 for students. How many students are on the bus if a total of $1,668 was collected from the 70 passengers?

  7. Marie has $5.05 in quarters and dimes. The number of quarters exceeds twice the number of dimes by one. Find the number she has of each kind.

  8. A class contributed $3.50 in nickels and dimes to the Red Cross. In all there were 45 coins. How many of each type of coin was contributed?

  9. Helen has $1.35 in her bank in nickels and dimes. There are 9 more nickels than dimes. Find the number of each.

  10. 353 people attend a local play at a private club. Members get tickets for $2.75, while non-members have to pay $6.50. If the total gate money for the play came to $1762, how many members and non-members came to the play?

  11. Eric has 130 coins consisting of nickels and quarters. The coins combined value comes to $ 15.90. Find out how many of each coin Eric has.

  12. Jim runs a food cart and during a busy outdoor festival he sold $7343.75 worth of food. He sells hot dogs for $2.95 and steak sandwiches for $9.95. If he sold a total of 985 items that day, how many of each item did he sell?

  13. Alice is counting a cash register at the end of the night. She has $1015 in $5 bills and $10 bills. If she has 138 bills altogether, how many of each type does she have?

  14. Jackie wants to make a mixture of nuts to sell in her store consisting of hazelnuts and cashews. Hazelnuts cost $6.50 per pound and cashews cost $4.50 per pound. If Jackie wants 60 pounds total mixture and the cost to be $5.10 per pound, how many pounds of each will she need?

  15. 586 people attend a banquet at Disney. Residents paid $12.95 and non-residents paid $17.95. If Disney made $9,423.70 from ticket sales for the event, how many residents and non-residents attended?

  16. Lou wants to make a coffee mixture to sell. He is going to mix Sumatra Coffee which cost $2.50 per pound with Columbian coffee which costs $3.75 per pound. He wants to make 50 pounds of mix and he wants the cost of the mix to be $3.35 per pound. How many pounds of each will he need?

  17. Jane invests $9,885 in two accounts. A savings account earns 6% interest, while a money market account earns 9.5% interest. After one year she made $696.35 interest from both accounts. How much did she invest in each account?

  18. TASK: REAL LIFE SYSTEMS OF LINEAR EQUATIONS In your groups, select three problems from the word problems given to demonstrate your knowledge of how to apply systems of linear equations to solve problems. You must choose one coin problem, one money problem and one mixture problem. Divide your poster board into three sections. Rewrite the problems that you decide to solve. Solve the problems step by step. Have a brief explanation as to how your group solved your problems. Use pictures to illustrate. Work neatly. Be ready to share your ideas.

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