10 Solving Problems Involving Literal Equations.pptx

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1. Solving Problems MATATAG 7 Grade involving Literal Equations P = 2l + 2w C=πd A= bh

2. OBJECTIVE solve problems involving literal equations and algebraic formulas

3. Literal Equation Literal equation is an equation that contains two or more variables. P = 2l + 2w I=Prt V=lwh d = rt A= bh C=πd Review

4. Solving Problems Involving Literal Equations A = 36 Example 1: Given: The area of a triangle has the formula A= bh. If the area of a triangular flag is 36 square inches and its base is 9 inches, find its height. , b = 9 Solution: , h = ? Formula: A= bh A = bh (2) (2) 2A = bh b b = h b 2A h = b 2A Solve h in terms of A: Substitute the given: h = b 2A h = 9 2 (36) h = 72 9 h = 8 in The height of the triangle is 8 inches.

5. Solving Problems Involving Literal Equations P = 120 Example 2: Given: The perimeter of a rectangle has the formula P=2l+2w. Find the width of a garden if the perimeter is 120 m and the length is 40 m. , l = 40 Solution: , w = ? Formula: P = 2l + 2w Solve w in terms of P: Substitute the given: The width of the garden is 20 meters -2l P = 2l + 2w -2l 2 P-2l = 2w 2 P-2l 2 = w w = P-2l 2 or P 2 - l w = P-2l 2 w = -2 2 120 (40) w = 2 120 - 80 w = 40 2 w = 20 m

6. C=πd Solving Problems Involving Literal Equations C = 35 Example 3: Given: Find the diameter of a circular lid if the circumference is 35 centimeters. (Use π=3.14, round your answer to two decimal places) , π=3.14 Solution: , d = ? Formula: C=πd π = d π C d = π C Solve d in terms of C: Substitute the given: d = π C 3.14 35 d ≈11.15 cm The diameter of the circular lid is 11.15 centimeters. π d =

7. P = 4s Solving Problems Involving Literal Equations P = 240 Example 4: Given: The perimeter of a square window is 240 cm. Find the length of one side. Solution: , s = ? Formula: P = 4s = s 4 P s = 4 P Solve s in terms of P: Substitute the given: s = 4 P 240 s = 60 cm The length of one side of the window is 60 centimeters. 4 s = 4 4

8. Solving Problems Involving Literal Equations a = 6 Example 5: Given: Two sides of a triangle have lengths of 6 dm and 9 dm. The perimeter is 24 dm. Find the length of the third side. , b = 9 Solution: , c = ? Formula: P = a + b + c Solve c in terms of P: Substitute the given: c = P - a - b The length of the third side of the triangle is 9 decimeters. c = P = a + b + c -a -a P-a = b + c -b - b P-a-b = c c = P - a - b 24 - 6 - 9 , P = 24 c = 18 - 9 c = 9 dm

9. Solving Problems Involving Literal Equations A = 70 Example 6: Given: The area of a rectangular field is 70 square meters. The width of the field is 10 meters. Find its length. , w = 10 Solution: , l = ? Formula: A = lw Solve l in terms of A: Substitute the given: The length of the rectangular field is 7 meters. A = lw w w = l w A l = w A l = w A l = 70 10 l = 7 m

10. Solving Problems Involving Literal Equations M = 29 Example 7: Given: If Marco’s age is 5 more than twice Carlos’s age, how old is Carlos if Marco is 29 years old? Solution: , C = ? Formula/ Equation: M = Solve C in terms of M: Substitute the given: C = 2 M-5 C = 29 C = 12 Let C be Carlos’s age and M be Marco’s age. 2C + 5 M = 2C + 5 -5 -5 M-5 = 2C 2 2 M-5 2 = C M-5 2 C = -5 2 C = 24 2 Carlos is 12 years old.

11. Thank You for Listening P = 2l + 2w C=πd A= bh

12. Activity Solve the the following problems involving algebraic equation. Use x to represent the variable. 1. Find the diameter of a circular rug if the circumference is 42 cm. (Use π=3.14 and round your answer to two decimal places) 2. The area of a triangular signboard is 48 square inches. If its base is 12 inches, find its height. 3. The perimeter of a rectangle is 150 meters. If its length is 50 meters, find its width. 4. The perimeter of a square-shaped table is 60 cm. Find the length of one side. 5. Two sides of a triangle have lengths of 7 m and 12 m. The perimeter is 30 m. Find the length of the third side. 6. A rectangular pool has an area of 72 square meters. If the width is 8 meters, find the length. 7. If Leah’s age is 6 more than three times Jonas’s age, how old is Jonas if Leah is 27 years old?

13. Answers 1. 2.

14. Answers 3. 4.

15. Answers 5. 6.

16. Answers 7.