1. LINEAR SYSTEMS – Word Problems There are 3 types of problems we will look at : 1. Plane / Boat problems 2. Money problems 3. Number problems

2. LINEAR SYSTEMS – Word Problems There are 3 types of problems we will look at : 1. Plane / Boat problems 2. Money problems 3. Number problems PLANE / BOAT problems ALWAYS use this format :

3. LINEAR SYSTEMS – Word Problems There are 3 types of problems we will look at : 1. Plane / Boat problems 2. Money problems 3. Number problems PLANE / BOAT problems ALWAYS use this format Once we fill in the given information, use the addition method to solve for ( x, y )

4. LINEAR SYSTEMS – Word Problems PLANE / BOAT problems ALWAYS use this format Fill in the given information… EXAMPLE : A plane travels 600 miles in 2 hours with the wind. It makes the return trip in 3 hours against the wind. Find the speed of the plane “x “ in no wind, and “y” the speed of the wind

5. LINEAR SYSTEMS – Word Problems PLANE / BOAT problems - distance = 600 Fill in the given information… EXAMPLE : A plane travels 600 miles in 2 hours with the wind. It makes the return trip in 3 hours against the wind. Find the speed of the plane “x “ in no wind, and “y” the speed of the wind

6. LINEAR SYSTEMS – Word Problems PLANE / BOAT problems - short time = 2 hours Fill in the given information… EXAMPLE : A plane travels 600 miles in 2 hours with the wind. It makes the return trip in 3 hours against the wind. Find the speed of the plane “x “ in no wind, and “y” the speed of the wind

7. LINEAR SYSTEMS – Word Problems PLANE / BOAT problems - long time = 3 hours Fill in the given information… EXAMPLE : A plane travels 600 miles in 2 hours with the wind. It makes the return trip in 3 hours against the wind. Find the speed of the plane “x “ in no wind, and “y” the speed of the wind

8. LINEAR SYSTEMS – Word Problems PLANE / BOAT problems Simplify the fractions… EXAMPLE : A plane travels 600 miles in 2 hours with the wind. It makes the return trip in 3 hours against the wind. Find the speed of the plane “x “ in no wind, and “y” the speed of the wind 300 200

9. LINEAR SYSTEMS – Word Problems PLANE / BOAT problems Our new equations … EXAMPLE : A plane travels 600 miles in 2 hours with the wind. It makes the return trip in 3 hours against the wind. Find the speed of the plane “x “ in no wind, and “y” the speed of the wind

10. LINEAR SYSTEMS – Word Problems PLANE / BOAT problems Addition method … EXAMPLE : A plane travels 600 miles in 2 hours with the wind. It makes the return trip in 3 hours against the wind. Find the speed of the plane “x “ in no wind, and “y” the speed of the wind +

11. LINEAR SYSTEMS – Word Problems PLANE / BOAT problems Solve for “x” … EXAMPLE : A plane travels 600 miles in 2 hours with the wind. It makes the return trip in 3 hours against the wind. Find the speed of the plane “x “ in no wind, and “y” the speed of the wind + Speed of plane in no wind…

12. LINEAR SYSTEMS – Word Problems PLANE / BOAT problems EXAMPLE : A plane travels 600 miles in 2 hours with the wind. It makes the return trip in 3 hours against the wind. Find the speed of the plane “x “ in no wind, and “y” the speed of the wind Speed of the wind Speed of plane in no wind… Substitute to find “y”

13. LINEAR SYSTEMS – Word Problems There are 3 types of problems we will look at : 1. Plane / Boat problems 2. Money problems 3. Number problems MONEY problems Count Equation how many items were sold ? Money Equation what are the prices of the items AND how much $$$ was collected ?

14. LINEAR SYSTEMS – Word Problems EXAMPLE : The boy scouts sold chips for $0.50 and pretzels for $0.75 at a recent camping outing. If they collected $94.50 and sold 154 items, how many bags of chips ( x ) and pretzels ( y ) were sold ? MONEY problems Count Equation how many items were sold ? Money Equation what are the prices of the items AND how much $$$ was collected ?

15. LINEAR SYSTEMS – Word Problems EXAMPLE : The boy scouts sold chips for $0.50 and pretzels for $0.75 at a recent camping outing. If they collected $94.50 and sold 154 items, how many bags of chips ( x ) and pretzels ( y ) were sold ? MONEY problems Count Equation how many items were sold ? Money Equation what are the prices of the items AND how much $$$ was collected ? Find the given information and place in the correct equations…

16. LINEAR SYSTEMS – Word Problems EXAMPLE : The boy scouts sold chips for $0.50 and pretzels for $0.75 at a recent camping outing. If they collected $94.50 and sold 154 items, how many bags of chips ( x ) and pretzels ( y ) were sold ? MONEY problems Count Equation how many items were sold ? Money Equation what are the prices of the items AND how much $$$ was collected ? Find the given information and place in the correct equations…

17. LINEAR SYSTEMS – Word Problems EXAMPLE : The boy scouts sold chips for $0.50 and pretzels for $0.75 at a recent camping outing. If they collected $94.50 and sold 154 items, how many bags of chips ( x ) and pretzels ( y ) were sold ? MONEY problems Count Equation how many items were sold ? Money Equation what are the prices of the items AND how much $$$ was collected ? Find the given information and place in the correct equations…

18. LINEAR SYSTEMS – Word Problems EXAMPLE : The boy scouts sold chips for $0.50 and pretzels for $0.75 at a recent camping outing. If they collected $94.50 and sold 154 items, how many bags of chips ( x ) and pretzels ( y ) were sold ? I like to use the addition method

19. LINEAR SYSTEMS – Word Problems EXAMPLE : The boy scouts sold chips for $0.50 and pretzels for $0.75 at a recent camping outing. If they collected $94.50 and sold 154 items, how many bags of chips ( x ) and pretzels ( y ) were sold ? Multiplied top equation by – 0.50

20. LINEAR SYSTEMS – Word Problems EXAMPLE : The boy scouts sold chips for $0.50 and pretzels for $0.75 at a recent camping outing. If they collected $94.50 and sold 154 items, how many bags of chips ( x ) and pretzels ( y ) were sold ? Add the two equations +

21. LINEAR SYSTEMS – Word Problems EXAMPLE : The boy scouts sold chips for $0.50 and pretzels for $0.75 at a recent camping outing. If they collected $94.50 and sold 154 items, how many bags of chips ( x ) and pretzels ( y ) were sold ? Solve for “y” +

22. LINEAR SYSTEMS – Word Problems EXAMPLE : The boy scouts sold chips for $0.50 and pretzels for $0.75 at a recent camping outing. If they collected $94.50 and sold 154 items, how many bags of chips ( x ) and pretzels ( y ) were sold ? Solve for “y” +

23. LINEAR SYSTEMS – Word Problems EXAMPLE : The boy scouts sold chips for $0.50 and pretzels for $0.75 at a recent camping outing. If they collected $94.50 and sold 154 items, how many bags of chips ( x ) and pretzels ( y ) were sold ? Substitute for “y” into either original equation and solve for “x”… +

24. LINEAR SYSTEMS – Word Problems There are 3 types of problems we will look at : 1. Plane / Boat problems 2. Money problems 3. Number problems When working on number problems look for key words such as sum, total, difference, twice, even / odd, etc. to create your equations. Then use either the substitution method or addition method to find your answers.

25. LINEAR SYSTEMS – Word Problems When working on number problems look for key words such as sum, total, difference, twice, even / odd, etc. to create your equations. Then use either the substitution method or addition method to find your answers. EXAMPLE : The sum of two numbers is 24. Their difference is 16. Find the two numbers

26. LINEAR SYSTEMS – Word Problems When working on number problems look for key words such as sum, total, difference, twice, even / odd, etc. to create your equations. Then use either the substitution method or addition method to find your answers. EXAMPLE : The sum of two numbers is 24. Their difference is 16. Find the two numbers

27. LINEAR SYSTEMS – Word Problems When working on number problems look for key words such as sum, total, difference, twice, even / odd, etc. to create your equations. Then use either the substitution method or addition method to find your answers. EXAMPLE : The sum of two numbers is 24. Their difference is 16. Find the two numbers

28. LINEAR SYSTEMS – Word Problems EXAMPLE : The sum of two numbers is 24. Their difference is 16. Find the two numbers + Addition method…

29. LINEAR SYSTEMS – Word Problems EXAMPLE : The sum of two numbers is 24. Their difference is 16. Find the two numbers + Solve for “x”

30. LINEAR SYSTEMS – Word Problems EXAMPLE : The sum of two numbers is 24. Their difference is 16. Find the two numbers + Substitute for “x” in either equation and solve for “y”…

31. LINEAR SYSTEMS – Word Problems EXAMPLE # 2 : The sum of two numbers is 27. The second number is three more than twice the first number.

32. LINEAR SYSTEMS – Word Problems EXAMPLE # 2 : The sum of two numbers is 27. The second number is three more than twice the first number.

33. LINEAR SYSTEMS – Word Problems EXAMPLE # 2 : The sum of two numbers is 27. The second number is three more than twice the first number.

34. LINEAR SYSTEMS – Word Problems EXAMPLE # 2 : The sum of two numbers is 27. The second number is three more than twice the first number. I will use substitution method…

35. LINEAR SYSTEMS – Word Problems EXAMPLE # 2 : The sum of two numbers is 27. The second number is three more than twice the first number. Solve for “x”… +

36. LINEAR SYSTEMS – Word Problems EXAMPLE # 2 : The sum of two numbers is 27. The second number is three more than twice the first number. Substitute for “x” and solve for “y’… +