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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Welcome back damarisnjambi2024 — missed you this week. Here are the solutions to the problems from Practice Work 7.3: 1. Nyambura's Age Step 1: Define variables and set up equations. Let Halima's age be H years. Let Nyambura's age be N years. From the problem: N = 3H (Nyambura is three times as old as Halima) N + H = 36 (The sum of their ages is 36) Step 2: Substitute the first equation into the second. Substitute N = 3H into N + H = 36: 3H + H = 36 4H = 36 Step 3: Solve for Halima's age (H). H = (36)/(4) H = 9 Step 4: Solve for Nyambura's age (N). N = 3H N = 3 × 9 N = 27 Nyambura is 27 years old. 2. Classroom Numbers Step 1: Define variables and set up equations. Let the number of girls be G. Let the number of boys be B. Let the number of teachers be T. From the problem: B = G + 2 (Boys are 2 more than girls) T = B - 10 (Teachers are 10 less than boys) B + G + T = 27 (Total people in class) Step 2: Express B and T in terms of G. Substitute B = G + 2 into T = B - 10: T = (G + 2) - 10 T = G - 8 Step 3: Substitute B and T (in terms of G) into the total people equation. (G + 2) + G + (G - 8) = 27 3G - 6 = 27 Step 4: Solve for G. 3G = 27 + 6 3G = 33 G = (33)/(3) G = 11 Step 5: Calculate B and T. B = G + 2 = 11 + 2 = 13 T = G - 8 = 11 - 8 = 3 There are 13 boys, 11 girls, and 3 teachers. 3. Consecutive Numbers Step 1: Define the consecutive numbers. Let the first number be x. The second number is x + 1. The third number is x + 2. Step 2: Set up the equation for their sum. x + (x + 1) + (x + 2) = 72 3x + 3 = 72 Step 3: Solve for x. 3x = 72 - 3 3x = 69 x = (69)/(3) x = 23 Step 4: Find the three consecutive numbers. First number: 23 Second number: 23 + 1 = 24 Third number: 23 + 2 = 25 The three consecutive numbers are 23, 24, and 25. 4. Price of Trousers and Shirt Step 1: Define variables and set up equations. Let the price of a shirt be S. Let the price of a pair of trousers be T. From the problem: T = 2S (Trousers are twice the price of a shirt) T + S = 1200 (Total cost is sh 1 200) Step 2: Substitute the first equation into the second. Substitute T = 2S into T + S = 1200: 2S + S = 1200 3S = 1200 Step 3: Solve for the price of the shirt (S). S = (1200)/(3) S = 400 The price of the shirt is sh 400. 5. Farmer's Animals Step 1: Define variables and set up equations. Let the number of sheep be S. Let the number of goats be G. Let the number of cows be C. From the problem: G = S + 15 (15 more goats than sheep) C = 3S (3 times as many cows as sheep) S + G + C = 75 (Total animals) Step 2: Express G and C in terms of S. G = S + 15 C = 3S Step 3: Substitute G and C (in terms of S) into the total animals equation. S + (S + 15) + 3S = 75 5S + 15 = 75 Step 4: Solve for S. 5S = 75 - 15 5S = 60 S = (60)/(5) S = 12 Step 5: Calculate the number of cows (C). C = 3S C = 3 × 12 C = 36 The farmer has 36 cows. Drop the next question! 📸