In a theatre group, the ratio of males to females is 2:3. On one Tuesday training, 10 male members were absent and six new female members joined the group as guests for the day. If on this day the rat

Hey Mohaa — ready when you are. The image contains two questions. I will solve question 15. Question 15: In a theatre group, the ratio of males to females is 2:3. On one Tuesday training, 10 male members were absent and six new female members joined the group as guests for the day. If on this day the ratio of males to females was 1:3, how many regular members does the group have? Step 1: Define variables for the initial number of male and female members. Let M be the initial number of male members and F be the initial number of female members. The initial ratio of males to females is 2:3. (M)/(F) = (2)/(3) This means M = 2k and F = 3k for some constant k. Step 2: Express the number of males and females on the specific Tuesday. On Tuesday, 10 male members were absent, so the number of males present was M - 10. Six new female members joined, so the number of females present was F + 6. Step 3: Set up the ratio for Tuesday. On this day, the ratio of males to females was 1:3. (M - 10)/(F + 6) = (1)/(3) Step 4: Substitute M = 2k and F = 3k into the Tuesday ratio equation. (2k - 10)/(3k + 6) = (1)/(3) Step 5: Solve the equation for k. Cross-multiply: 3(2k - 10) = 1(3k + 6) 6k - 30 = 3k + 6 Subtract 3k from both sides: 3k - 30 = 6 Add 30 to both sides: 3k = 36 Divide by 3: k = (36)/(3) k = 12 Step 6: Calculate the initial number of male and female members. Initial number of males M = 2k = 2(12) = 24. Initial number of females F = 3k = 3(12) = 36. Step 7: Calculate the total number of regular members. The total number of regular members is M + F. Total regular members = 24 + 36 = 60. The group has 60 regular members. The final answer is 60. Send me the next one 📸