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.
ScanSolve AI Answer
Okay, let's solve these problems. Question 5: In a class of 59 pupils, there are 7 more boys than girls. How many boys are in that class? Step 1: Define variables and set up equations. Let B be the number of boys and G be the number of girls. The total number of pupils is 59: B + G = 59 (1) There are 7 more boys than girls: B = G + 7 (2) Step 2: Substitute equation (2) into equation (1). (G + 7) + G = 59 2G + 7 = 59 Step 3: Solve for G. 2G = 59 - 7 2G = 52 G = (52)/(2) G = 26 Step 4: Solve for B using the value of G. B = G + 7 B = 26 + 7 B = 33 There are 33 boys in the class. The answer is: 33 boys Question 6: Peter spent (1)/(4) of his money on biscuits and (1)/(2) of the rest on bananas. What fraction is left? Step 1: Calculate the fraction of money remaining after buying biscuits. Fraction spent on biscuits = (1)/(4) Fraction remaining = 1 - (1)/(4) = (4)/(4) - (1)/(4) = (3)/(4) Step 2: Calculate the fraction of money spent on bananas. Peter spent (1)/(2) of the rest on bananas. Fraction spent on bananas = (1)/(2) × (3)/(4) = (3)/(8) Step 3: Calculate the total fraction of money spent. Total fraction spent = Fraction on biscuits + Fraction on bananas Total fraction spent = (1)/(4) + (3)/(8) To add these, find a common denominator, which is 8: (1)/(4) = (1 × 2)/(4 × 2) = (2)/(8) Total fraction spent = (2)/(8) + (3)/(8) = (5)/(8) Step 4: Calculate the fraction of money left. Fraction left = 1 - Total fraction spent Fraction left = 1 - (5)/(8) = (8)/(8) - (5)/(8) = (3)/(8) The answer is: (3)/(8) Question 7: If 21 students can weed a farm in 4 hours. How many students can weed the farm in 3(1)/(2) hours? Step 1: Identify the relationship between students and time. This is an inverse proportion problem: as the number of students increases, the time taken to weed the farm decreases. Let S_1 = 21 students and T_1 = 4 hours. Let S_2 be the unknown number of students and T_2 = 3(1)/(2) hours = 3.5 hours. Step 2: Set up the inverse proportion equation. S_1 × T_1 = S_2 × T_2 Step 3: Substitute the known values and solve for S_2. 21 × 4 = S_2 × 3.5 84 = 3.5 S_2 S_2 = (84)/(3.5) S_2 = (840)/(35) S_2 = 24 24 students can weed the farm in 3(1)/(2) hours. The answer is: 24 students Question 8: A man bought 80 eggs and discovered that 20 were bad. What percentage of the eggs was good? Step 1: Calculate the number of good eggs. Total eggs = 80 Bad eggs = 20 Good eggs = Total eggs - Bad eggs = 80 - 20 = 60 Step 2: Calculate the fraction of good eggs. Fraction of good eggs = Number of good eggsTotal eggs = (60)/(80) Step 3: Convert the fraction to a percentage. Percentage of good eggs = (60)/(80) × 100\% Percentage of good eggs = (6)/(8) × 100\% Percentage of good eggs = (3)/(4) × 100\% Percentage of good eggs = 0.75 × 100\% Percentage of good eggs = 75\% The answer is: 75\% Question 9: The distance round a square plot is 36m. What is the area of the plot? Step 1: Calculate the length of one side of the square. The distance round a square plot is its perimeter. Perimeter of a square = 4 × side Given Perimeter = 36 m 4 × side = 36 m side = (36)/(4) m side = 9 m Step 2: Calculate the area of the square plot. Area of a square = side × side Area = 9 m × 9 m Area = 81 m^2 The answer is: 81 m^2 3 done, 2 left today. You're making progress.