University:
Georgia Southern University
Course:
MATH 2242 | Calculus II
Academic year:

2024
Views:

122

Pages:

5
Author:

Jarrett Brock

Question 1 What percent 20 is of 80? Answer 1 20 80 = 1 4 = 0.25 80 20 = 4 1 =0.25 0.25 is 25%. Answer 2 Let 80 be 100%, and 20 = ?. We have to multiply 20 by 100% and divide by 80. 20 × 100 % 80 = 2000 % 80 = 25 % . 80 20×100% = 80 2000% =25%. Answer 3 20 is 25% of 80. Question 2 Write 19/25 as a percentage. Answer 1 19 25 × 4 = 76 100 = 76 % . 25 19 ×4= 100 76 =76%. Answer 2 19 25 = 76 % . 25 19 =76%. Answer 3 19 25 × 100 = 76. 25 19 ×100=76. Thus, the answer is 76%. Question 3 To solve: The proportion 𝑦 10 = 13 4 10 y = 4 13 . Answer 1 Approach: The quotient of two numbers is called a ratio. Example: 5 7 or 5 : 7. 7 5 or 5:7. The ratio can also be expressed as fractional notation. To solve a proportion: If two ratios are equal, then: 𝑎 𝑏 = 𝑐 𝑑 . b a = d c . Use cross multiplication to find the unknown. Calculation: Determine 𝑦 y: 𝑦 10 = 13 4 . 10 y = 4 13 . Cross multiply: 𝑦 ⋅ 4 = 13 ⋅ 10. y⋅4=13⋅10. 4 𝑦 = 130. 4y=130. Divide both sides by 4: 𝑦 = 130 4 = 32.5. y= 4 130 =32.5. The value of 𝑦 y is 32.5. Answer 2 Step 1: Multiply both sides by 10: 𝑦 = 13 4 × 10. y= 4 13 ×10. Simplify: 𝑦 = 13 ⋅ 10 4 . y= 4 13⋅10 . Simplify the fraction: 𝑦 = 130 4 = 65 2 = 32.5. y= 4 130 = 2 65 =32.5. Answer 3 Step 1: Cross-multiply: 𝑦 10 = 13 4 . 10 y = 4 13 . Cross product: 𝑦 × 4 = 10 × 13. y×4=10×13. 4 𝑦 = 130. 4y=130. Solve for 𝑦 y: 𝑦 = 32.5. y=32.5. Question 4 Whether the given ratios are equivalent ratios or not. Given: The ratios are 3 7 7 3 and 18 42 42 18 . Answer 1 Calculation: Cross multiply to check: 3 × 42 = 18 × 7. 3×42=18×7. Simplify: 126 = 126. 126=126. Thus, the ratios are equivalent. Answer 2 Step 1: Find the least common denominator (LCM) of 42 and 7, which is 42. Rewrite the fractions with denominator 42: For 3 7 7 3 : 3 × 6 7 × 6 = 18 42 . 7×6 3×6 = 42 18 . Since both fractions are 18 42 42 18 , the ratios are equivalent. Answer 3 18 42 = 6 × 3 6 × 7 = 3 7 . 42 18 = 6×7 6×3 = 7 3 . Thus, the two ratios are equivalent. Question 5 Which three ratios are equivalent to 12 to 9? Answer 1 Step 1: Divide both sides by a common factor: 12 9 = 4 3 . 9 12 = 3 4 . Multiply both sides by a factor (e.g., 2 or 3): 12 × 2 : 9 × 2 = 24 : 18 , 12×2:9×2=24:18, 12 × 1 1 3 : 9 × 1 1 3 = 16 : 12. 12×1 3 1 :9×1 3 1 =16:12. Thus, the three equivalent ratios are: 4:3 24:18 16:12. Answer 2 Step 1: The ratio 12 9 9 12 can be simplified to 4 3 3 4 . Multiply by different factors: 4 × 5 : 3 × 5 = 20 : 15 , 4×5:3×5=20:15, 4 × 6 : 3 × 6 = 24 : 18 , 4×6:3×6=24:18, 4 × 3 : 3 × 3 = 12 : 9. 4×3:3×3=12:9. Thus, the equivalent ratios are: 4:3 20:15 24:18. Answer 3 Divide numerator and denominator by 3: 12 9 = 4 3 . 9 12 = 3 4 . Multiply by 2, 3, and 4: 4 × 2 : 3 × 2 = 8 : 6 , 4×2:3×2=8:6, 4 × 3 : 3 × 3 = 12 : 9 , 4×3:3×3=12:9, 4 × 4 : 3 × 4 = 16 : 12. 4×4:3×4=16:12. Thus, the equivalent ratios are: 8:6 12:9 16:12.