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
Step 1: Solve Question 6 (top left) a) To find the total value of the digit 8 in 84,265,739, we identify its place value. The digit 8 is in the ten millions place. Value of 8 = 8 × 10,000,000 = 80,000,000 The total value of the digit 8 is Sh. 80,000,000. b) To round off 84,265,739 to the nearest million shillings, we look at the digit in the millions place (4) and the digit to its right (2, in the hundred thousands place). Since 2 is less than 5, we round down, keeping the millions digit as 4 and changing all digits to its right to zero. Rounded amount = 84,000,000 The rounded amount is Sh. 84,000,000. Step 2: Solve Question 7 (top right) a) Ben's age is t years and is "not less than 14 years". This means her age is greater than or equal to 14. t 14 The inequality is t 14. b) To illustrate the inequality t 14 on a number line, we draw a closed circle at 14 (indicating that 14 is included) and an arrow extending to the right (indicating all values greater than 14). Number line illustration: cccccccccccccccc & & & & & & & & & & & & & & & \\ 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 (The line should extend from 14 to the right, with a solid circle at 14). Step 3: Solve Question 5 (middle left) Let j be the cost of one jacket and s be the cost of one shirt. From the problem statement, we can form two linear equations: 1. Gideon: 3j + 2s = 4600 2. John: 2j + 3s = 4400 To solve this system of equations, we can use the elimination method. Multiply Equation 1 by 2 and Equation 2 by 3 to make the coefficients of j equal: 2 × (3j + 2s) = 2 × 4600 6j + 4s = 9200 (Equation 3) 3 × (2j + 3s) = 3 × 4400 6j + 9s = 13200 (Equation 4) Subtract Equation 3 from Equation 4: (6j + 9s) - (6j + 4s) = 13200 - 9200 5s = 4000 s = (4000)/(5) s = 800 Now substitute the value of s into Equation 1: 3j + 2(800) = 4600 3j + 1600 = 4600 3j = 4600 - 1600 3j = 3000 j = (3000)/(3) j = 1000 The cost of each jacket is Sh. 1000 and the cost of each shirt is Sh. 800. Step 4: Solve Question 8 (middle right) Total attendees = 5024. Learners were (5)/(8) of the total attendees: Number of learners = (5)/(8) × 5024 = 5 × 628 = 3140 Remaining attendees after learners: Remaining attendees = 5024 - 3140 = 1884 Parents were (2)/(3) of the remaining attendees: Number of parents = (2)/(3) × 1884 = 2 × 628 = 1256 The rest were community members. Number of community members = Remaining attendees - Number of parents Number of community members = 1884 - 1256 = 628 There were 628 community members. Step 5: Solve Question 6 (bottom left - algebraic equation) Given the algebraic equation: (6t-2)+3(7-2t)=18 First, distribute the 3 into the parenthesis: 6t - 2 + (3 × 7) - (3 × 2t) = 18 6t - 2 + 21 - 6t = 18 Combine like terms (6t and -6t, and -2 and 21): (6t - 6t) + (-2 + 21) = 18 0t + 19 = 18 19 = 18 This statement is a contradiction, meaning there is no value of t that can satisfy the given equation. The equation has no solution. Step 6: Solve Question 9 (bottom right) An employee earns Sh. 3600 for working 5 days. First, calculate the daily earning rate: Daily earning rate = Total earningsNumber of days = 3600 Sh.5 days = 720 Sh./day Now, calculate the earnings for 12 days at the same rate: Earnings for 12 days = Daily earning rate × 12 days Earnings for 12 days = 720 Sh./day × 12 days Earnings for 12 days = 8640 Sh. The employee will earn Sh. 8640 after working for 12 days. Send me the next one 📸