Basic Algebraic Applications Day 1 Steps for Solving

Basic Algebraic Applications Day 1

Steps for Solving Basic Algebraic Applications 1. 2. 3. 4. 5. 6. 7. Read the Problem What are they asking? Define Unknowns and variables What operations do you have? Key concepts and operations Set up the problem Solve the equation Verify that you answered the question correctly. (Does your answer make sense? ) Check your answer

Solving Algebraic Applications Is about … Solving word problems with unknown values. Procedures Application 1. Read the problem 1. The length of a rectangle is 2 km less than width. The perimeter is 68 km. 3 times the width km How long is each side. 2. What are they asking? Define Unknowns and variables 2. Both sides are needed. Width (w) and length (ℓ). ℓ in terms of w, w = w 3. What operations do you have? Key concepts and operations 3. Rectangle (□), is (=), less than (-), times (x), perimeter (add all the sides) = 68 km 4. Set up the problem. Draw figure if necessary. . 4. ℓ = 3 w - 2 w w ℓ = 3 w - 2 w + ℓ + w + ℓ = 68 w + (3 w -2) + w + (3 w -2) = 68

5. Solve the equation 5. w + (3 w -2) + w + (3 w -2) = 68 6. Verify that you answered the question correctly. (Does your answer make sense? ) 6. Solving for length and width, so length is Needed. ℓ = 3 w -2 ℓ = 3(9) – 2 w=9 ℓ = 27 – 2 ℓ = 25 w = 9 km & ℓ = 25 km 7. Check your answer 7. w + ℓ + w + ℓ = 68 9 + 25 + 9 +25 ? 68 68 = 68 ☺

Application Procedures 1. Read the problem 1. One side of a triangle is 3 cm shorter than a second side. The remaining side is 5 cm longer than the second side. The perimeter is 38 cm cm. Find the length of each side. 2. What are they asking? Define Unknowns and variables 2. All sides are needed. side a 2 nd side 1 st side: b remaining side: side c 3. What operations do you have? Key concepts and operations 3. triangle (Δ), is (=), shorter than (-), longer than (+), perimeter (add all the sides) = 38 cm 4. Set up the problem. Draw figure if necessary. . 4. a = b --3 3 b c = b ++5 5 a + b + c = 38 (b - 3) + b + (b + 5) = 38

5. Solve the equation 5. (b - 3) + b + (b + 5) = 38 6. Solving for all three sides, so two sides must still be found. c = b +5 b = 12 a = b - 3 (b - 3) + b + (b + 5) = 38 6. Verify that you answered the question correctly. (Does your answer make sense? ) a = (12) – 3 c =(12) +5 a= 9 c= 17 a = 9 cm, b = 12 cm, c = 17 cm 7. Check your answer 7. a + b + c = 38 9 + 12+ 17 ? 38 38 = 38 ☺