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
You're on a roll — Item 2: a) Help Aisha to determine the date in the near future on which they can hold the party. Step 1: Determine the frequency of Aisha's and Zaharah's visits. Aisha visits every 3 days. Zaharah visits every 5 days. Step 2: Find the least common multiple (LCM) of their visiting frequencies to determine when they will visit together again. The LCM of 3 and 5 is 3 × 5 = 15. They will visit their parents together every 15 days. Step 3: Calculate the date of their next combined visit. Their first visit together was on 1st June 2025. The next visit will be 15 days after 1st June 2025. 1 st June + 15 days = 16 th June The date they can hold the party is 16th June 2025. b) Determine the amount Aisha borrowed. Step 1: Determine the ratio of their contributions based on their ages. Aisha is twice as old as Zaharah. Let Zaharah's age be Z. Then Aisha's age is 2Z. The ratio of Aisha's contribution to Zaharah's contribution is 2Z : Z = 2 : 1. Step 2: Calculate Aisha's total contribution. Zaharah contributes 65,000. Since Aisha's contribution is twice Zaharah's contribution: Aisha's contribution = 2 × Zaharah's contribution Aisha's contribution = 2 × 65,000 = 130,000 Step 3: Calculate the amount Aisha borrowed. Aisha borrowed 35% of her contribution. Amount borrowed = 35\% of 130,000 Amount borrowed = (35)/(100) × 130,000 Amount borrowed = 35 × 1300 = 45,500 The amount Aisha borrowed is 45,500. c) Help Zaharah to find the actual 4-digit PIN to use. Step 1: Convert the given base ten number to base five. The PIN is the base five representation of 179 (base 10). Divide 179 by 5 repeatedly and record the remainders. 179 ÷ 5 = 35 remainder 4 35 ÷ 5 = 7 remainder 0 7 ÷ 5 = 1 remainder 2 1 ÷ 5 = 0 remainder 1 Step 2: Read the remainders from bottom to top to get the base five number. The PIN is 1204_5. The actual 4-digit PIN to use is 1204_5. d) Determine the time they will both take to wash the plates. Step 1: Determine the individual work rates. Aisha can wash the plates in 4 hours. Her rate is (1)/(4) of the work per hour. Zaharah can wash the plates in 6 hours. Her rate is (1)/(6) of the work per hour. Step 2: Calculate their combined work rate. When working together, their rates add up. Combined rate = Aisha's rate + Zaharah's rate Combined rate = (1)/(4) + (1)/(6) Find a common denominator, which is 12. Combined rate = (3)/(12) + (2)/(12) = (5)/(12) of the work per hour Step 3: Calculate the time taken to complete the work together. Time taken = Total workCombined rate. Since total work is 1 (representing all plates): Time taken = (1)/(5)12 = (12)/(5) hours Step 4: Convert the time to hours and minutes. (12)/(5) hours = 2 (2)/(5) hours To convert (2)/(5) hours to minutes: (2)/(5) × 60 minutes = 2 × 12 minutes = 24 minutes The time they will both take to wash the plates is 2 hours and 24 minutes. Got more? Send 'em!