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
Here's how to solve the problem: Task a) How much should Lydia expect to earn from the contract? Step 1: Determine the total contract amount. The total contract amount is eighteen million six hundred forty-five thousand shillings. Total contract amount = 18,645,000 shillings Step 2: Calculate the total percentage allocated for materials and transport. Materials: 45\% Transport: 0.3 = 30\% Total percentage for materials and transport = 45\% + 30\% = 75\% Step 3: Calculate the percentage remaining for Lydia's earnings (salary). Percentage for earnings = 100\% - 75\% = 25\% Step 4: Calculate Lydia's expected earnings. Lydia's earnings = 25\% × 18,645,000 Lydia's earnings = 0.25 × 18,645,000 = 4,661,250 shillings Lydia should expect to earn 4,661,250 shillings. Task b) Help the bride to determine the new amount they have to pay for decoration. Step 1: Identify the original contract amount. Original contract amount = 18,645,000 shillings Step 2: Apply the increase ratio. An increase in payment of 3:2 means the new payment is (3)/(2) times the original payment. New payment = (3)/(2) × Original contract amount Step 3: Calculate the new payment amount. New payment = (3)/(2) × 18,645,000 New payment = 1.5 × 18,645,000 = 27,967,500 shillings The new amount the bride has to pay is 27,967,500 shillings. Task c) Help Lydia to determine the number of table clothes she will get from her rolls. Step 1: List the lengths of the material rolls. The lengths are 320 m, 480 m, and 520 m. Step 2: Find the greatest common divisor (GCD) of the lengths to determine the maximum possible length for each table cloth. Prime factorization of each length: 320 = 2^6 × 5 480 = 2^5 × 3 × 5 520 = 2^3 × 5 × 13 The common prime factors are 2^3 and 5. GCD = 2^3 × 5 = 8 × 5 = 40 m So, each table cloth will be 40 m long. Step 3: Calculate the number of table clothes from each roll. From the 320 m roll: (320)/(40) = 8 table clothes From the 480 m roll: (480)/(40) = 12 table clothes From the 520 m roll: (520)/(40) = 13 table clothes Step 4: Calculate the total number of table clothes. Total table clothes = 8 + 12 + 13 = 33 Lydia will get a total of 33 table clothes. Send me the next one 📸