Here are the solutions to the math problems: 13. The average mass of 3 girls is 45kg. Two of them weigh 42kg and 47kg. Find the mass of the third girl. 14. Find the L.C.M. 8, 10, 12.

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Asked on April 30, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-04-30T22:57:36.335Z

Here are the solutions to the math problems: 13. The average mass of 3 girls is 45kg. Two of them weigh 42kg and 47kg. Find the mass of the third girl. Step 1: Calculate the total mass of the three girls. The average mass is the total mass divided by the number of girls. Total mass = Average mass × Number of girls Total mass = 45 kg × 3 = 135 kg Step 2: Calculate the combined mass of the two known girls. Combined mass = 42 kg + 47 kg = 89 kg Step 3: Find the mass of the third girl. Mass of third girl = Total mass - Combined mass of two girls Mass of third girl = 135 kg - 89 kg = 46 kg The correct option is c. 46 kg 14. Find the L.C.M. 8, 10, 12. Step 1: Find the prime factorization of each number. 8 = 2 × 2 × 2 = 2^3 10 = 2 × 5 12 = 2 × 2 × 3 = 2^2 × 3 Step 2: Identify the highest power of each prime factor present. The prime factors are 2, 3, and 5. Highest power of 2: 2^3 (from 8) Highest power of 3: 3^1 (from 12) Highest power of 5: 5^1 (from 10) Step 3: Multiply these highest powers together to find the L.C.M. L.C.M. = 2^3 × 3^1 × 5^1 = 8 × 3 × 5 = 24 × 5 = 120 The correct option is a. 120 15. Express 28:42 as a fraction in its simplest form. Step 1: Write the ratio as a fraction. 28:42 = (28)/(42) Step 2: Find the greatest common divisor (GCD) of the numerator and denominator. Factors of 28: 1, 2, 4, 7, 14, 28 Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 The GCD of 28 and 42 is 14. Step 3: Divide both the numerator and the denominator by their GCD. (28 ÷ 14)/(42 ÷ 14) = (2)/(3) The correct option is not explicitly listed as a fraction, but 2:3 is equivalent to (2)/(3). (2)/(3) 16. 3/5 = x/20. What is x? Step 1: Set up the proportion. (3)/(5) = (x)/(20) Step 2: Solve for x by cross-multiplication. 3 × 20 = 5 × x 60 = 5x Step 3: Divide to find x. x = (60)/(5) x = 12 The correct option is e. 12 17. Express 7(1)/(2)\% as a fraction in its simplest form. Step 1: Convert the mixed percentage to an improper fraction. 7(1)/(2)\% = (7 × 2 + 1)/(2)\% = (15)/(2)\% Step 2: Convert the percentage to a fraction by dividing by 100. (15)/(2)\% = (15)/(2 × 100) = (15)/(200) Step 3: Simplify the fraction. Find the greatest common divisor (GCD) of 15 and 200. Both are divisible by 5. (15 ÷ 5)/(200 ÷ 5) = (3)/(40) The correct option is d. (3)/(40) 18. Express 0.275 as a percentage. Step 1: Multiply the decimal by 100 to convert it to a percentage. 0.275 × 100\% = 27.5\% The correct option is a. 27.5\% 19. Express 1291 as a decimal. Explanation: The question "Express 1291 as a decimal" typically means to write the integer with a decimal point, which is 1291.0. However, given the options and common question patterns, it's highly probable that the question implicitly means "Express (1291)/(1000) as a decimal" or similar. Based on the handwritten work in the image, it seems to imply division by 1000. Step 1: Assume the question implies (1291)/(1000). (1291)/(1000) = 1.291 The correct option is a. 1.291 20. 1(1)/(2) - (1)/(3) × (1)/(3) Step 1: Convert the mixed number to an improper fraction. 1(1)/(2) = (1 × 2 + 1)/(2) = (3)/(2) Step 2: Perform the multiplication first (following order of operations). (1)/(3) × (1)/(3) = (1 × 1)/(3 × 3) = (1)/(9) Step 3: Perform the subtraction. (3)/(2) - (1)/(9) Find a common denominator, which is 18. (3 × 9)/(2 × 9) - (1 × 2)/(9 × 2) = (27)/(18) - (2)/(18) (27 - 2)/(18) = (25)/(18) Step 4: Convert the improper fraction to a mixed number (optional, but often preferred for final answers). (25)/(18) = 1(7)/(18) The correct option is b, which is 2(47)/(50) (incorrect) or c, which is 1(1)/(4) (incorrect). Let's recheck the options. Option 'b' is 2(47)/(50), option 'c' is 1(1)/(4), option 'd' is 4/5, option 'e' is 1(7)/(18). So 'e' is the correct option. 1(7)/(18) 21. The marks in a history test are awarded out of 75. If a girl scored 64%, how many marks did she get? Step 1: Convert the percentage to a decimal. 64\% = (64)/(100) = 0.64 Step 2: Calculate the marks obtained. Marks obtained = Percentage score × Total marks Marks obtained = 0.64 × 75 Marks obtained = 48 The correct option is c. 48 22. There are 500 pupils in a school. If 275 are boys, what percentage are girls? Step 1: Calculate the number of girls. Number of girls = Total pupils - Number of boys Number of girls = 500 - 275 = 225 Step 2: Calculate the percentage of girls. Percentage of girls = Number of girlsTotal pupils × 100\% Percentage of girls = (225)/(500) × 100\% Percentage of girls = 0.45 × 100\% = 45\% The correct option is c. 45\% **23. A sack containing coconuts weighed 460g. When more coconuts were added the weight was increased by 2

Accepted Answer · 2026-04-30T22:57:36.335Z

Here are the solutions to the math problems: 13. The average mass of 3 girls is 45kg. Two of them weigh 42kg and 47kg. Find the mass of the third girl. Step 1: Calculate the total mass of the three girls. The average mass is the total mass divided by the number of girls. Total mass = Average mass × Number of girls Total mass = 45 kg × 3 = 135 kg Step 2: Calculate the combined mass of the two known girls. Combined mass = 42 kg + 47 kg = 89 kg Step 3: Find the mass of the third girl. Mass of third girl = Total mass - Combined mass of two girls Mass of third girl = 135 kg - 89 kg = 46 kg The correct option is c. 46 kg 14. Find the L.C.M. 8, 10, 12. Step 1: Find the prime factorization of each number. 8 = 2 × 2 × 2 = 2^3 10 = 2 × 5 12 = 2 × 2 × 3 = 2^2 × 3 Step 2: Identify the highest power of each prime factor present. The prime factors are 2, 3, and 5. Highest power of 2: 2^3 (from 8) Highest power of 3: 3^1 (from 12) Highest power of 5: 5^1 (from 10) Step 3: Multiply these highest powers together to find the L.C.M. L.C.M. = 2^3 × 3^1 × 5^1 = 8 × 3 × 5 = 24 × 5 = 120 The correct option is a. 120 15. Express 28:42 as a fraction in its simplest form. Step 1: Write the ratio as a fraction. 28:42 = (28)/(42) Step 2: Find the greatest common divisor (GCD) of the numerator and denominator. Factors of 28: 1, 2, 4, 7, 14, 28 Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 The GCD of 28 and 42 is 14. Step 3: Divide both the numerator and the denominator by their GCD. (28 ÷ 14)/(42 ÷ 14) = (2)/(3) The correct option is not explicitly listed as a fraction, but 2:3 is equivalent to (2)/(3). (2)/(3) 16. 3/5 = x/20. What is x? Step 1: Set up the proportion. (3)/(5) = (x)/(20) Step 2: Solve for x by cross-multiplication. 3 × 20 = 5 × x 60 = 5x Step 3: Divide to find x. x = (60)/(5) x = 12 The correct option is e. 12 17. Express 7(1)/(2)\% as a fraction in its simplest form. Step 1: Convert the mixed percentage to an improper fraction. 7(1)/(2)\% = (7 × 2 + 1)/(2)\% = (15)/(2)\% Step 2: Convert the percentage to a fraction by dividing by 100. (15)/(2)\% = (15)/(2 × 100) = (15)/(200) Step 3: Simplify the fraction. Find the greatest common divisor (GCD) of 15 and 200. Both are divisible by 5. (15 ÷ 5)/(200 ÷ 5) = (3)/(40) The correct option is d. (3)/(40) 18. Express 0.275 as a percentage. Step 1: Multiply the decimal by 100 to convert it to a percentage. 0.275 × 100\% = 27.5\% The correct option is a. 27.5\% 19. Express 1291 as a decimal. Explanation: The question "Express 1291 as a decimal" typically means to write the integer with a decimal point, which is 1291.0. However, given the options and common question patterns, it's highly probable that the question implicitly means "Express (1291)/(1000) as a decimal" or similar. Based on the handwritten work in the image, it seems to imply division by 1000. Step 1: Assume the question implies (1291)/(1000). (1291)/(1000) = 1.291 The correct option is a. 1.291 20. 1(1)/(2) - (1)/(3) × (1)/(3) Step 1: Convert the mixed number to an improper fraction. 1(1)/(2) = (1 × 2 + 1)/(2) = (3)/(2) Step 2: Perform the multiplication first (following order of operations). (1)/(3) × (1)/(3) = (1 × 1)/(3 × 3) = (1)/(9) Step 3: Perform the subtraction. (3)/(2) - (1)/(9) Find a common denominator, which is 18. (3 × 9)/(2 × 9) - (1 × 2)/(9 × 2) = (27)/(18) - (2)/(18) (27 - 2)/(18) = (25)/(18) Step 4: Convert the improper fraction to a mixed number (optional, but often preferred for final answers). (25)/(18) = 1(7)/(18) The correct option is b, which is 2(47)/(50) (incorrect) or c, which is 1(1)/(4) (incorrect). Let's recheck the options. Option 'b' is 2(47)/(50), option 'c' is 1(1)/(4), option 'd' is 4/5, option 'e' is 1(7)/(18). So 'e' is the correct option. 1(7)/(18) 21. The marks in a history test are awarded out of 75. If a girl scored 64%, how many marks did she get? Step 1: Convert the percentage to a decimal. 64\% = (64)/(100) = 0.64 Step 2: Calculate the marks obtained. Marks obtained = Percentage score × Total marks Marks obtained = 0.64 × 75 Marks obtained = 48 The correct option is c. 48 22. There are 500 pupils in a school. If 275 are boys, what percentage are girls? Step 1: Calculate the number of girls. Number of girls = Total pupils - Number of boys Number of girls = 500 - 275 = 225 Step 2: Calculate the percentage of girls. Percentage of girls = Number of girlsTotal pupils × 100\% Percentage of girls = (225)/(500) × 100\% Percentage of girls = 0.45 × 100\% = 45\% The correct option is c. 45\% **23. A sack containing coconuts weighed 460g. When more coconuts were added the weight was increased by 2

Here are the solutions to the math problems: 13. The average mass of 3 girls is 45kg. Two of them weigh 42kg and 47kg. Find the mass of the third girl. 14. Find the L.C.M. 8, 10, 12.

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Here are the solutions to the math problems: 13. The average mass of 3 girls is 45kg. Two of them weigh 42kg and 47kg. Find the mass of the third girl. 14. Find the L.C.M. 8, 10, 12.

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