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ScanSolve AI Answer
Question 11: b) Find the: (i) value of m; (ii) number of people who speak one language only. To solve this, we will use the information provided in the problem statement for Question 11, which was: Total people = 50 Speak Yoruba (Y): (m^2 + 3) Speak Hausa (H): (5m - 3) Speak Igbo (I): (3m + 1) Speak all three languages (Y H I): 4 Speak exactly two languages: 14 Those who speak Igbo and Yoruba only (Y I only) are half of those who speak Yoruba and Hausa only (Y H only). Those who speak Hausa and Igbo only (H I only) are 1 less than those who speak Yoruba and Hausa only (Y H only). 6 of them could not speak any of the languages. --- b) (i) Find the value of m. Step 1: Define variables for the 'exactly two languages' regions. Let x be the number of people who speak Yoruba and Hausa only (Y H only). From the problem statement: • Those who speak Igbo and Yoruba only (Y I only) are half of those who speak Yoruba and Hausa only: Y I only = (1)/(2)x. • Those who speak Hausa and Igbo only (H I only) are 1 less than those who speak Yoruba and Hausa only: H I only = x - 1. Step 2: Use the total number of people speaking exactly two languages to find x. The problem states that 14 people speak exactly two languages. (Y H only) + (Y I only) + (H I only) = 14 x + (1)/(2)x + (x - 1) = 14 Combine like terms: 2.5x - 1 = 14 Add 1 to both sides: 2.5x = 15 Divide by 2.5: x = (15)/(2.5) = 6 So, the number of people speaking exactly two languages are: $Y H