1. **State the problem:** We have two shops offering discounts on the same phone. We want to find: a) Which shop offers the lower price. b) The difference in the offer prices between the two shops. 2. **Formulas and rules:** - To find the offer price after a discount, use: $$\text{Offer Price} = \text{Original Price} \times (1 - \text{Discount Rate})$$ - Discount rate should be expressed as a decimal (e.g., 1/3 = 0.333..., 20% = 0.20). 3. **Calculate Low-cost Larry's offer price:** - Original price: £90 - Discount: 1/3 off means discount rate = $\frac{1}{3} \approx 0.3333$ - Offer price: $$90 \times (1 - \frac{1}{3}) = 90 \times \frac{2}{3} = 60$$ 4. **Calculate Markdown Market's offer price:** - Original price: £78 - Discount: 20% off means discount rate = 0.20 - Offer price: $$78 \times (1 - 0.20) = 78 \times 0.80 = 62.4$$ 5. **Compare the offer prices:** - Low-cost Larry's price: £60 - Markdown Market's price: £62.4 - Lower price is at Low-cost Larry's. 6. **Calculate the difference in offer prices:** $$62.4 - 60 = 2.4$$ The phone is £2.4 cheaper at Low-cost Larry's. **Final answers:** - a) The offer price is lower at Low-cost Larry's. - b) The difference in offer price is £2.4.