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LINEAR SYSTEMS – Word Problems There are 3 types of problems we will look at : 1. Plane / Boat problems 2. Money problems 3. Number problems 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 : distance x y short time distance x y long time 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 distance x y short time distance x y long time Once we fill in the given information, use the addition method to solve for ( x , y ) LINEAR SYSTEMS – Word 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 PLANE / BOAT problems ALWAYS use this format distance x y short time distance x y long time Fill in the given information… LINEAR SYSTEMS – Word 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 PLANE / BOAT problems - distance = 600 600 x y short time 600 x y long time Fill in the given information… LINEAR SYSTEMS – Word 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 PLANE / BOAT problems - short time = 2 hours 600 x y 2 600 x y long time Fill in the given information… LINEAR SYSTEMS – Word 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 PLANE / BOAT problems - long time = 3 hours Fill in the given information… 600 x y 2 600 x y 3 LINEAR SYSTEMS – Word 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 PLANE / BOAT problems 300 600 x y 2 600 x y 3 200 Simplify the fractions… LINEAR SYSTEMS – Word 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 PLANE / BOAT problems x y 300 x y 200 Our new equations … LINEAR SYSTEMS – Word 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 PLANE / BOAT problems + x y 300 x y 200 2x 500 Addition method … LINEAR SYSTEMS – Word 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 PLANE / BOAT problems x y 300 + x y 200 2x 2 Solve for “x” … 500 2 x 250 Speed of plane in no wind… LINEAR SYSTEMS – Word 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 PLANE / BOAT problems x y 300 250 y 300 250 250 y 50 x 250 Speed of the wind Speed of plane in no wind… Substitute to find “y” 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 ? x y total count of items Money Equation what are the prices of the items AND how much $$$ was collected ? price x price y total $$$ collected 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 ? x y total count of items Money Equation what are the prices of the items AND how much $$$ was collected ? price x price y total $$$ collected 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 Find the given information and place in the correct equations… Count Equation how many items were sold ? x y total count of items Money Equation what are the prices of the items AND how much $$$ was collected ? price x price y total $$$ collected 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 ? x y 154 MONEY problems Find the given information and place in the correct equations… Count Equation how many items were sold ? x y total count of items Money Equation what are the prices of the items AND how much $$$ was collected ? price x price y total $$$ collected 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 ? x y 154 0.50 x 0.75 y 94.50 MONEY problems Find the given information and place in the correct equations… Count Equation how many items were sold ? x y total count of items Money Equation what are the prices of the items AND how much $$$ was collected ? price x price y total $$$ collected 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 ? x y 154 0.50 x 0.75 y 94.50 I like to use the addition method 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 ? 0.50x y 154 0.50 x 0.75 y 94.50 0.50 x 0.50 y 77.00 Multiplied top equation by – 0.50 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 ? 0.50 x y 154 + 0.50 x 0.75 y 94.50 0.50 x 0.50 y 77.00 0.25 y 17.50 Add the two equations 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 ? + 0.50x y 154 0.50 x 0.75 y 94.50 0.50 x 0.50 y 77.00 0.25 y 17.50 0.25 y 17.50 0.25 0.25 Solve for “y” 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 ? + 0.50 x y 154 0.50 x 0.75 y 94.50 0.50 x 0.50 y 77.00 0.25 y 17.50 0.25 y 17.50 0.25 0.25 y 70 Solve for “y” 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 ? + 0.50 x y 154 0.50 x 0.75 y 94.50 0.50 x 0.50 y 77.00 0.25 y 17.50 0.25 y 17.50 0.25 0.25 y 70 x y 154 x 70 154 x 84 Substitute for “y” into either original equation and solve for “x”… 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. LINEAR SYSTEMS – Word Problems EXAMPLE : The sum of two numbers is 24. Their difference is 16. Find the two numbers 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. LINEAR SYSTEMS – Word Problems EXAMPLE : The sum of two numbers is 24. Their difference is 16. Find the two numbers x y 24 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. LINEAR SYSTEMS – Word Problems EXAMPLE : The sum of two numbers is 24. Their difference is 16. Find the two numbers x y 24 x y 16 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. LINEAR SYSTEMS – Word Problems EXAMPLE : The sum of two numbers is 24. Their difference is 16. Find the two numbers + x y 24 x y 16 2 x 40 Addition method… LINEAR SYSTEMS – Word Problems EXAMPLE : The sum of two numbers is 24. Their difference is 16. Find the two numbers + x y 24 x y 16 2 x 40 Solve for “x” 2 x 40 2 2 x 20 LINEAR SYSTEMS – Word Problems EXAMPLE : The sum of two numbers is 24. Their difference is 16. Find the two numbers + x y 24 x y 16 2 x 40 2 x 40 2 2 x 20 Substitute for “x” in either equation and solve for “y”… x y 24 20 y 24 y4 LINEAR SYSTEMS – Word Problems EXAMPLE # 2 : The sum of two numbers is 27. The second number is three more than twice the first number. LINEAR SYSTEMS – Word Problems EXAMPLE # 2 : The sum of two numbers is 27. The second number is three more than twice the first number. x y 27 LINEAR SYSTEMS – Word Problems EXAMPLE # 2 : The sum of two numbers is 27. The second number is three more than twice the first number. x y 27 y 2x 3 LINEAR SYSTEMS – Word Problems EXAMPLE # 2 : The sum of two numbers is 27. The second number is three more than twice the first number. x y 27 y 2x 3 I will use substitution method… x 2x 3 27 LINEAR SYSTEMS – Word Problems EXAMPLE # 2 : The sum of two numbers is 27. The second number is three more than twice the first number. x y 27 y 2x 3 x 2x 3 27 x 2 x 3 27 3x 3 27 3 3 + 3x 24 x 8 Solve for “x”… LINEAR SYSTEMS – Word Problems EXAMPLE # 2 : The sum of two numbers is 27. The second number is three more than twice the first number. x y 27 y 2x 3 x 2x 3 27 x 2 x 3 27 3x 3 27 3 3 + 3x 24 x 8 Substitute for “x” and solve for “y’… 8 y 27 y 19

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