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Solving Worded Problems (with simultaneous equations)

Slideshow 20, Mathematics Mr Richard Sasaki, Room 307. Solving Worded Problems (with simultaneous equations). Objectives. Understand how to represent single linear equations with worded problems and solve Be able to solve simultaneous equations with two unknowns. Worded Representation.

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Solving Worded Problems (with simultaneous equations)

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  1. Slideshow 20, Mathematics Mr Richard Sasaki, Room 307 Solving Worded Problems(with simultaneous equations)

  2. Objectives • Understand how to represent single linear equations with worded problems and solve • Be able to solve simultaneous equations with two unknowns

  3. Worded Representation Solving single equations for one unknown should be no problem by now. All we need to know is how to represent them! Example Ms. Morita goes to a shop and buys three bananas. She pays with a 500 Yen coin and receives 350 Yen in change. How much did each banana cost? Try to look at what she gave equal to what she received. So each banana cost 50 Yen. = +

  4. Worded Representation Let’s try another. Example Yui swaps three trading cards for a trading card and 70 Yen. How much is a trading card worth on average? + = = Try the worksheets! A trading card is worth 35 Yen.

  5. Answers 12 + 2000 = 50000, ticket: 4000 Yen 4 = 500, A bar is worth 125 Yen 4 = 320, A mouse has 80kcal. 3 + 114 = 120, ride: 2 min + 70 = 200, the drink cost 130 Yen. 142 = 568, tea: 4 min 3 = 1260, a kitten is 420g. 4 = 2 + 5200 ornament: 2600 Yen 4 = 120, he uses 30ml of dye each time. 2 = 240, pack: 120 Yen 6 = 24, A jar has 4 spiders. 15 = 120, strawberry: 8 Yen 4 = 7.2, a balloon has 1.8l of air.

  6. Simultaneous Equations Worded expressions can also lead to simultaneous equations. Example On one day, a man buys 4 hammers and 10 screws for 1250 Yen. On another day he buys 2 hammers and 40 screws for 800 Yen. How much do the hammers and screws cost?

  7. Simultaneous Equations Then just solve the equations. ① ② So a hammer costs 300 Yen and a screw costs 5 Yen. 2 x ② 2 x ② - ① ①

  8. Simultaneous Equations Example A farmer is told that three sheep and four cows are worth 200,000 Yen. However, 8 sheep minus the value of a cow are worth 125000 Yen.

  9. Simultaneous Equations ① ② Try the worksheets! 4 x ② So a sheep is worth 20,000 Yen and a cow is worth 35,000 Yen. 4 x ② + ① ①

  10. Answers Sweet: 20 Yen, Toy: 50 Yen y = 48, 2 + 2y = 32 Length: 12, width: 4 Shoes: 6000 Yen, Hat 2000 Yen Beach: 5000 Yen, Tokyo: 2000 Yen Impossible. = 54/17, y = -29/17 Cat: 5kg Dog: 6kg

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