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.
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Here are the solutions to the problems: Question (a): To find the value of y, we use the information about pupils who did not pass Maths. Step 1: Identify the regions representing pupils who did not pass Maths. Based on the visible parts of the Venn diagram and common problem structures, we assume: • Pupils who passed only Maths: y • Pupils who passed only the other subject (let's call it Science): y+2 • Pupils who passed both subjects: y-2 • Pupils who passed neither subject: 2 Pupils who did not pass Maths are those who passed only Science and those who passed neither subject. So, the number of pupils who did not pass Maths is (y+2) + 2. Step 2: Set up the equation based on the given information. We are given that 23 pupils did not pass Maths. (y+2) + 2 = 23 Step 3: Solve the equation for y. y + 4 = 23 y = 23 - 4 y = 19 The value of y is 19. Question (b): To find the probability of picking a pupil who likes both subjects, we need the number of pupils who like both and the total number of pupils. Step 1: Calculate the number of pupils who like both subjects. The number of pupils who like both subjects is represented by y-2. Substitute the value of y=19: Number who like both = 19 - 2 = 17 Step 2: Calculate the total number of pupils. The total number of pupils is the sum of all regions in the Venn diagram: Total pupils = y + (y+2) + (y-2) + 2 Substitute y=19: Total pupils = 19 + (19+2) + (19-2) + 2 Total pupils = 19 + 21 + 17 + 2 Total pupils = 59 Step 3: Calculate the probability. The probability is the ratio of pupils who like both subjects to the total number of pupils. Probability = Number who like bothTotal pupils Probability = (17)/(59) The probability is (17)/(59). Question (Tea Problem): To find the total amount of tea prepared, we need to calculate the amount of milk and then add it to the amount of water. Step 1: Identify the given amount of water and the relationship between milk and water. Amount of water (W) = 12 litres. Milk (M) was 20% more than water, which can be expressed as M = W + 0.20W = 1.20W. Step 2: Calculate the amount of milk. M = 1.20 × W M = 1.20 × 12 litres M = 14.4 litres Step 3: Calculate the total amount of tea prepared. The total amount of tea is the sum of the ✂️ _That answer was long and got cut off. Reply continue and I'll finish it._