**Unformatted text preview: **MATH 1053 – Quantitative Methods for Business Week 1 Lecture Exercise & Solution Lecture exercise A store purchases a coffee maker from the manufacturer and then offers it for sale at 40% mark up on the cost price. After virtually no customer interest for three months, the manager decides to sell the coffee maker for a 10% discount off the marked‐up price. If a customer pays $252, what is the (percentage) profit or loss that the store has made on this item? Follow the ‘Problem Solving Steps’. Solution 1. Modelling step: Mark up rate Rm = 40% Discount rate Rd = 10% Discount price DP = $252 Cost price CP = ? Mark up price MP = ? Percentage profit/loss = ? Percentage profit/loss = (DP – CP)/CP × 100% MP = CP × (1 + Rm) (Equation 1) DP = MP × (1 – Rd) (Equation 2) 1 2. Solving step: Use Equation 2 to find the mark up price MP: 252 = MP × (1 – 0.1) MP = 252/0.9 = 280 Use Equation 1 to find the cost price CP: 280 = CP × (1 + 0.4) CP = 280/1.4 = 200 Calculate percentage profit/loss: Percentage profit/loss = (252 – 200)/200 × 100% = 26% (positive so profit) 3. Interpreting step: The store has made a 26% profit from selling the coffee maker at 10% discount on the mark up price. 2 ...

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