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 are the solutions to the questions: a) How you used the money he gave you. Step 1: Let the total money given by the guardian be M. Money used for sugar = (2)/(5)M. Step 2: Calculate the remaining money after buying sugar. Remaining money = M - (2)/(5)M = (3)/(5)M. Step 3: Calculate the money used for buying rice. Money for rice = (5)/(9) of the remaining money. Money for rice = (5)/(9) × (3)/(5)M = (15)/(45)M = (1)/(3)M. Step 4: Calculate the total fraction of money spent on sugar and rice. Total fraction spent = (2)/(5)M + (1)/(3)M = (6)/(15)M + (5)/(15)M = (11)/(15)M. Step 5: Determine the fraction of money deposited. The money deposited is the balance. Fraction deposited = M - (11)/(15)M = (4)/(15)M. Step 6: Calculate the total money given, since UGX 40,000 was deposited. We know that (4)/(15)M = UGX 40,000. M = 40,000 × (15)/(4) M = 10,000 × 15 M = 150,000 The total money given was UGX 150,000. Step 7: Show the breakdown of how the money was used. Money for sugar = (2)/(5) × 150,000 = UGX 60,000. Money for rice = (1)/(3) × 150,000 = UGX 50,000. Money deposited = UGX 40,000. Total spent and deposited = 60,000 + 50,000 + 40,000 = UGX 150,000. b) How you obtained the correct pin. Step 1: Convert the given code 78 (base 10) to base four. Divide 78 by 4 and record the remainders. 78 ÷ 4 = 19 remainder 2 19 ÷ 4 = 4 remainder 3 4 ÷ 4 = 1 remainder 0 1 ÷ 4 = 0 remainder 1 Step 2: Read the remainders from bottom to top to get the base four number. The PIN is 1032_4. The correct PIN is 1032. That's 2 down. 3 left today — send the next one.