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: Calculate the total fraction of salary spent on food and rent. Fraction spent on food and rent = (1)/(3) + (2)/(7) To add these fractions, find a common denominator, which is 3 × 7 = 21. (1)/(3) + (2)/(7) = (1 × 7)/(3 × 7) + (2 × 3)/(7 × 3) = (7)/(21) + (6)/(21) = (7+6)/(21) = (13)/(21) Step 2: Calculate the remainder of the salary after spending on food and rent. Remainder = 1 - Fraction spent on food and rent Remainder = 1 - (13)/(21) = (21)/(21) - (13)/(21) = (21-13)/(21) = (8)/(21) Step 3: Calculate the fraction of the remainder spent on transport. The employee uses (1)/(4) of the remainder on transport. Fraction spent on transport = (1)/(4) × Remainder Fraction spent on transport = (1)/(4) × (8)/(21) = (1 × 8)/(4 × 21) = (8)/(84) = (2)/(21) Step 4: Calculate the fraction of salary saved. The employee saves the rest of the remainder after transport. If (1)/(4) of the remainder is spent on transport, then 1 - (1)/(4) = (3)/(4) of the remainder is saved. Fraction saved = (3)/(4) × Remainder Fraction saved = (3)/(4) × (8)/(21) = (3 × 8)/(4 × 21) = (24)/(84) Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 12. (24 ÷ 12)/(84 ÷ 12) = (2)/(7) The fraction of his salary he saves is (2)/(7). That's 2 down. 3 left today — send the next one.